Preambule:
First and foremost the most important note of all: GregTech is an overhaul mod. It is not just an add-on that will come on top of other mods (mainly IC2): it has its own tech tree, its own progression curve, its own balance, and now a machine for every task. A lot of so-called nerfs in GregTech are just incentives for a more streamlined experience. 
For example, to tackle a lot of complaints: 
You can't make Charcoal from Wood because GT has its own Coke Oven to do so
Vanilla tools are heavily nerfed because GT has its own variations and each has its advantages
You cannot mix dust to get alloy dust (the most infamous being Copper Dust and Tin Dust mixed in Bronze Dust) because that's not how it works. You have to get these dusts to the appropriate temperature for them to mix.
You cannot use Iron to make Flint&Steel, because first it does not make sense because Steel is not the same thing as Iron, and second because there are a lot of other options for that, each again with their own advantages and drawbacks.
So if you ever feel constrained, or limited in a boring way (like grinding a lot of resources or just being in a technological dead-end), remember that in GT6 there might be an easier way: in GregTech you will progress slowly, but it will be fun.

General Notes:
NEI is GregTech best friend. GT has a lot of informations in its tooltips and recipes so being able to browse them is paramount. However, it can often show more recipes than are actually necessary or useful, as GregTech contains many, many 'recycling' recipes (which simply convert materials into different forms, or break apart machinery into the metals used to make it), and many recipes that can be produced yet because the basic materials are not setup to spawn in the world. One of the more important recipe category in NEI is "Combination smelting". You can browse this category when you search for an alloy ingot recipe (for instance Bronze). There's also a GT Book of Alloys in-game, but it's much more inconvenient because there's no search functionality in it, compared to NEI. Take the time to be familiar with the R/Left-click and U/Right-click shortcuts to quickly jump between items and their recipe/usage. 
GregTech ores generate in many forms, however the three that are the most useful are Small, Sand, and Gravel. Small Ores have a lower Mining Level than their regular versions, and when broken will drop either Crushed Ore or Dirty Dust (or a Gem if possible). Sand and Gravel Ores are mined with a Shovel rather than a Pickaxe, however much more importantly, will obey gravity and fall if unsupported. This can be exploited alongside the trick of 'place a torch to make an entire stack of falling sand drop as items' to mine Sand and Gravel Ores without the tool mining levels that would normally be required. Because of this property of Sand Ores, Desert biomes can make for good starting locations, as with little luck can an ore vein be found at the surface and easily gathered. 
The extended debug display can be opened by holding H after pressing F3. This display allows viewing the Melting and Boiling Points of all items that can be thrown into a Smelting Crucible, along with constituants. If you use NEI, another one of its perks is that you can cycle through chunk display modes with F9. The red lines are chunk corners, so mining straight down on these lines allow you to check the content of 4 chunks at once. In GT6 a vein spawns in every 3 chunks so if you arrange a digging matrix by using these red lines, you can easily map the locations of several veins around your base. Additionally since there's only one vein every 3 chunks you can stop digging as soon as you've reach a vein: there won't be another one under it (although there still might be sparse small ores beneath it). 
IndustrialCraft 2 Industrial TNT is crafted out of Flint and TNT. Industrial TNT can be crafted with String to make Dynamite items. When placed, Dynamite will break a 3x3x3 cube centered on the impact point, while not being dangerous at all, while ITNT will kill you if your near it when it explodes. This makes it extremely efficient for early-game mining of higher-level materials or excavating an underground area, provided you have enough Gunpowder. GT has its own flavour of dynamite but its based on Nitroglycerine. 
In GregTech Iron is not an early material so instead of regular Iron Buckets, you can start with Wooden Bucket to carry cool liquids like Water or Milk. Of course you won't be able to carry lava or any other melted material. Also please note that since Wooden Buckets are meant to place liquids into the world, you cannot drink from them. Use other means of bottling to drink. 
Skeletons have a small chance (1/16 by default) to fire a random GregTech Arrow in stead of a conventional arrow. This includes arrows tipped with radioactive materials, which cause Radiation Poisoning on hit. As such, carrying Milk can be a good idea to carry around, because Milk counter Radioactivity (but remember: not in a bucket because you can't drink from it!) 
One of the most valuable resources in the early game is loot. Metal armor found in dungeons/villages/mineshaft chests can be melted down and used for tools, once a Smelting Crucible has been crafted. It can easily be worthwhile to only use Leather armor, and damaged metal armor looted from monsters, just to get the extra metal to get off the ground. Beware that only pristine stuff can be smelted in a crucible: used tools, armor, or weapons cannot. GregTech also introduce its own version of dungeons, Strongholds, which is a big place with several rooms with a lot of loot in them. Thus exploring in GregTech can be a rewarding activity, too! 
Phosphorus Dust and Creosote Oil can be used to make Torches or Matches. 
A final general note: Creative mode is your best friend to experiment things. Energy types, Steam pipes, Recipes in the Crucible: there is a lot of complex things in GregTech and in the beginning it can be very difficult to understand all the intricacies of the mod. So keep a Creative mode world on the side to test stuff. Also this guide may become obsolete quite quickly because GT is updated every week, so take everything written here with a little bit of Salt. 

The Stone Age:
When you start a new map with GT6 you'll have to establish you base. But in doing so, take note of these pointers: 
- GT ores spawns either in veins (sometimes big ones) or lone ores that can be seen quite clearly if you have some wide space and few trees. As such a Desert is often the best place to start a base. Bonus point if there's a Sand Lignite/Sand Coal vein there to help you start on fuel. Plus there's Jasper there, and being able to make Flint&Tinder will come in handy later. 
- Villages are also a valuable starting point because of their chests, which can contain precious materials you likely won't be able to craft yourself for a long time. The agriculture there is also a bonus, and trading with the villagers can help sometimes. 
- Spruce and Dark Oak Wood forests are best suited for GT axes (lots of vertical wood, even for big trees) and since you're going to need a lot of charcoal on a regular basis, having such resources at hand is valuable. Note that, like Dark Oak Wood, Spruce trees can be planted in a 2x2 fashion to have very big Spruce trees, ideal for GT Axes. 
Since you start in the Stone age, you'll have to act like a cave person: Flint tools will be you primary focus. In GT6 Flint has a fire aspect, which is very convenient because it allows you to light targets on fire, which kills them more easily and often cook meat when you kill animals. Flint tools may not have a lot of durability, but can be found in abundance (by the way note that villages have gravel paths). In addition to its killing potential, Flint is also the primary component for a mortar, and crafting mortars will be a daily routine for you until you start to build your first machines, and it won't happen soon. 
Certus Quartz is also a viable alternative for tools because it has the same Tier level as Iron, allowing you to mine ores that you would not have been able to mine with a Stone/Flint Pickaxe in the first place, even though mining beyond your means can be inefficient if you're not able to correctly use what you've gathered. 
Cobblestone Pickaxes, even though they have horrible durability (barely over ten Stone blocks), are really fast at mining Stone, so they are very good for branch or chunk mining (see general notes above), and they are basically free. Be careful though that GT replacement for Cobblestone pickaxes, like other Vanilla items, is not made the default to ensure compatibility with other mods that could use the replaced tools. To enable the GT recipes, you should look into Minetweaker scripts. 
You should also focus on your farming skills, since you'll be able to automate a lot of the food processing on that topic later on, and because farming is one of the only few renewable resources, you should take full advantage of it. 
Under GregTech 6, the only metals that can be smelted in a vanilla Furnace are Copper, Tin, Bronze, Lead, Zinc, and Bismuth. Of those materials, only Copper can be used to make tools. (Lead can be used, but it requires Tungstensteel Rods as handles). All other metals must be melted, often alloyed, and subsequently cast, in a Smelting Crucible (heated by a Burning Box) and Molds. 

Crafting your first crucible and learning the arts of smelting is of the utmost importance in playing GregTech 6. 

Smelting:
Smelting in a crucible is very basic, so basic there's not even a GUI for that. 
A crucible is a block that you place on top of a burning box, and in which you'll throw your ingredients. Lighting up fuel in your burning box will make it produce heat upwards, onto the crucible, which will heat up as well, until it reaches a temperature high enough to melt its ingredients...or itself. You better get used to that because a lot of contraptions in the beginning of GregTech are GUI-less, so nothing is handed out to you: you have to do the work by yourself, and only later will you be able to automate more and more steps of your work process. 
To begin, and to avoid going back and forth collecting materials, go on a mining operation to collect at least 80 Clay balls, some amount of Stone, Wood, Flint, and Coal, enough Copper and Tin to make at least 25 Copper ingots and 7 Tin ingots, and 8 ingots worth of either Lead, Bronze, or Bismuth. 
Copper and Tin cannot be directly combined to make Bronze. To combine them, smelt Copper and Tin Ores into Ingots, then use Flint and Stone to craft a Mortar, and use the Mortar to crush the Ingots into Dusts. Then, craft 3 Copper Dusts and 1 Tin Dust in a square to get 4 Bronze Dusts. 
Combine Stone and Sticks to make Hammers (more than one will likely be needed, as Stone Hammers have very low durability). Place a Hammer and two Bronze Ingots in a vertical line in your crafting grid to make a Double Ingot, then use the Hammer again with the Double Ingot to make a Bronze Plate. Two plates and a Stick combine to make a File. Craft another Bronze Ingot with the File to make a Bronze Rod. Combine a Plate, a Rod, a Stick, a Hammer, and a File to make a Chisel. Finally, craft six Bronze Ingots (in a Y-shape) with a Hammer in the center to make a Wrench. These are the mandatory initial tools to craft your first GregTech contraption: the Crucible. 
Note: Additional tool, not mandatory but highly recommended: Pincers. Items cast in a Mold will be extremely hot, cool slowly (100 kelvins/second), and cause severe damage to a player who attempts to remove them. Right-clicking with a set of Pincers allows a player to extract the hot items as soon as they solidify. You can also use Lead or Bismuth but remember that a tool durability follow its materials, so a Bronze tool will be way more durable that a Lead one. But that said, you'll need a lot of Bronze in your GregTech career, for tools and machines, whereas Lead or Bismuth will be of much lesser use by then. So it's up to you to decide which material to use, as it happens so many times in GT. 
Smelt 12 of the Clay balls into Bricks, combine the remaining Clay into Blocks, and smelt them into Hardened Clay. 7 Hardened Clay, a Hammer, and a Chisel combine to make a Ceramic Crucible. One Double Copper Plate (2 ingots + Hammer -> Double Ingot, + Hammer -> Plate; 2 Plates + Hammer -> Double Plate), 3 Brick Blocks, 4 Lead, Bronze, or Bismuth Plates, and a Wrench make a Burning Box. (Which of the three Burning Boxes crafted doesn't matter much yet; they serve the same purpose but work at different speeds/efficiency). Finally 5 Hardened Clay, a Chisel, and a Hammer craft into a Mold. 
The standard basic Smelting Crucible is made of Ceramic, because it has a quite high melting point, allowing you to melt a lot of different metals and alloys. Be wary though that because it's very light, it heat up and cool down very quickly. It's very easy to go overboard with a crucible and safety measures, although efficient, won't be able to save you every time. Standard molds are also made from Ceramic because of the same melting point reason, and because Clay is easy to find, especially if you're near a river, a beach or a swamp. 
Place the Crucible in a place that's not near anything flammable. Place the Burning Box directly below it, and make sure it has an air block in front of it. Place one or more Molds adjacent to the Crucible. 
Note: Initially Molds have no pattern in them. The shape of item created by a Mold is determined by what shape is Chiseled into it: molds are GUI-less too. Molds have 25 spaces within them, which must be knocked out in specific patterns to yield specific items; if an invalid pattern is given, the Mold will instead produce a number of Nuggets. The page on Molds has a full list of all valid patterns, and there is an in-game book that list all of them. To chisel a pattern into a Mold, right-click on its inner area with a Chisel. The chiseled piece will be knocked out of the Mold. Also note that removing Molds with a pickaxe should be made with caution because a mold entity that "jumps" in a crucible will be turned into Ceramic Scrap, rendering it useless. 
Note: Despite NEI only showing pure metals being thrown into a Crucible, any shape of metal can be thrown in. Chunks, Dirty Dusts, Crushed Ores, undamaged metal tools and armor, anything except Ore Blocks. However, throwing in items other than pure metals will usually also partially fill the Crucible with Stone, which must be removed before the material in the crucible can be useful. Material that has been thrown into a Crucible can be removed as Scrap by right-clicking while the Crucible is cold. Right-clicking to remove material from a heated Crucible will result in the player taking very significant damage, most of the time lethal. 
The Crucible is heated by the Burning Box under it. The material used to make the Box determines the rate at which it burns fuel, and its efficiency in doing so. However, to use the Burning Box, its fuel must be lit. Flint & Tinder is the GregTech equivalent of a Flint and Steel, but can be crafted using Flint and either an Iron nugget, Steel nugget, a gem of Quartz, Nether Quartz, Certus Quartz, or Chipped Jasper (uncommonly found in Deserts). Feed the Burning Box with fuel by right-clicking it with conventional Furnace fuel (Coal, Charcoal, Saplings, ...). (Note: Once fuel has been inserted, it cannot be removed while the Box is lit). Once the Box has Fuel, right-click it with the Flint & Tinder to try and light it. This will likely take multiple tries because Flint & Tinder does not have a 100% success rate, more like 30%. 
While active, the Burning Box will also periodically produce Ashes or Dark Ashes; right-click the Box with an empty hand to remove them (that's safe, you can do it while it's lit). Once lit, the Burning Box will continue to burn fuel until it runs out of it, or if its front side is blocked by an opaque block. This allows for an emergency shut-down, by placing a block of Dirt in front of an active Box. 
Now some important safety warnings: 
- An active Burning Box will cause nearby flammable objects to catch fire (around 4 blocks away). 
- Touching (right-clicking or touching it with your body) a heated Crucible, or a Mold containing hot cast metal, will result in the player taking very heavy damage. 
- If an item or material inside a Crucible reaches its Boiling Point, or if an item falls in that has no listed boiling point, it will vaporize, dealing heavy damage to all players and mobs near the Crucible. This can include Molds, or the Crucible itself. Note: as material vaporizes, the Mass inside the Crucible decreases, causing it to heat faster. If a Crucible vaporizes, it will also vaporize all material inside it, and set several random nearby blocks on fire. 
- Be extremely cautious around the "opaque block in front of the burning box" mechanic because a Burning Box will only shut down after it has burned its current fuel. So during your first experiences, prefer using Lignite, or even Saplings, to ensure that when you drop an opaque block in front of the Burning Box, it will stop quickly because it will have burned its current fuel quickly (Lignite and Saplings both are very inefficient fuel, compared to Coal and Charcoal). For instance if you put a Block of Coal in a Burning Box, light it, and immediately put a Dirt block in front of it, it won't shut down until it has burnt the whole block, which may heat your Crucible way past its melting point, vaporising its content and itself into nothingness, wasting everything. 
- Removing a Burning Box by using a wrench will stop it immediately, and will allow you to retrieve ashes and unburnt fuel, but you'll lose the currently burning fuel. This may be a safer emergency measure but be careful around touching the Crucible with your body, and remember that doing so use your wrench durability. 
Once the Burning Box below the Crucible is lit, it will start to heat the Crucible. The rate at which a Crucible heats depends upon the mass of the Crucible, and the mass of the metal inside it. Once the metal inside the Crucible melts, it can be casted into adjacent Molds by right-clicking the Mold. Note: The metal that will be casted into the mold is the one that has the highest melting point. For example if your crucible is at 1360K and contains 3 units of Bronze and 1 unit of Copper, Bronze will be casted first and only after the 3 Bronze units have been casted will the Copper be casted as well. This is an interesting mechanic when you're not following the recipes exactly (like if you have melted a lot of Tetrahedrite into Copper, mixed it with Tin to make Bronze, and retrieved the excess Copper after casting the Bronze) 

Some notes on Materials:
You can smelt meat into Meat Bars (ingots), which can then be used to make very nourishing Hamburgers. 
When in need, Chalcopyrite smelts as Copper, Cassiterite as Tin and Galena as Lead, and can all be smelted in a regular Furnace. 
The notable approximate temperatures for early metalworking are: Tin (550K), Lead (650K), Copper and Bronze (1350K), Iron (1800K), Wrought Iron (2000K), Steel (2050k), Titanium (1980K), Gold (1500K), Stone (vaporizes at 2000K), and Ceramic (Crucible vaporizes at 2500K). By knowing these melting and boiling points, Crucible temperature can be roughly observed by looking at the color of the liquified metal in the Crucible, until you craft a Thermometer. For instance if you mix Copper and Tin in a Crucible and heat it, you'll first see the liquid Tin (past 500K) and at some point later you'll see the Bronze (1350K). After you've poured the Bronze out of the Crucible, if there isn't any Bronze left, but there's still Copper, you'll see it liquefied (Bronze is a desaturated orange while Copper is a bright orange-red color). If there isn't Bronze nor Copper anymore, but there is Tin left, you'll see it liquefied (Tin is bright gray). 
When the Crucible cool down too much, and goes below the melting point of a material everything goes back to the darkish solid state. 
Note: If you've mixed different materials in the crucible, and if these materials does not all mix (like if you've thrown an Iron pickaxe, its Wood won't melt with its Iron regardless of the temperature), you'll never see the colored liquid state, whatever temperature the Crucible is, you'll only see the dark gray solid state. That's why you've have to respect recipes as much as possible until you can craft a thermometer. 
Iron smelting is a bit of a special issue to handle. The primary source of Iron is Magnetite (later on you'll encounter Yellow and Brown Limonite which are much more efficient to get iron from). Magnetite can be melted, but will not directly melt into Iron. In order to convert Magnetite into Iron, Dark Ashes must be mixed with the Magnetite. And as Dark Ashes can be most reliably obtained by running a Burning Box, you'll need to burn a fair bit of Coal or Lignite to get Dark Ashes for Iron. Luckily you'll have a lot of Bronze tools to craft in the beginning so burning Coal and Lignite to get Bronze will also yield Dark Ashes for you. Pyrite and legitimate Iron Ore are even better, but they're way harder to find. Hematite is easier to find but is a bit of a pain, because you have to smelt it with Dark Ashes AND Calcite (gotten from smelt marble). 
Steel requires temperatures of around 2050K with a ratio of one part Carbon for 50 parts of Wrought Iron (Note: don't consider melting whole ingots, but rather tiny dusts, because the Crucible can only have up to 16 units). You can extract Carbon from Graphite Ore by washing it in a Cauldron; small Graphite Ore is found below y-level 20. Alternatively and far more easily, find Steel tools in dungeon treasure chests and throw these into the Crucible. 
Hammers help you crush ores in crushed dusts (especially Copper and Tin that are found on a regular basis in caves), you'll get more material from an ore that way, especially if you wash them afterwards in a Cauldron. 
One final note, but I'll write that again in another topic: Rubber can me smelted in the Crucible. Rubber plates are in fact Rubber sheets. Following the same principle you can also make Rubber rings with liquid Rubber. Be careful because you waste a part of the material in the process though. It's one of the "hidden recipes" that does not appear in NEI because the Crucible and Molds are GUI-less, so feel free to experiment on your own. 
Before the Forge Age your current work process should more or less be: 
- Mining Ore (like Copper) or getting Impure Dusts from sparse Sand/Gravel Ores. 
- Crushing Ore to Crushed Dusts with hammers. 
The next step will be way more rewarding. 

The Forge Age:
Before diving in the wonderful world of machines and automation characterizing the Forge Age, you'll need some very convenient tools and contraptions. 
- An Iron Bucket. Made of 3 iron plates, 2 of them curved by hammering a plate on a rolling cylinder, it's your only way to carry Lava. Why would you want to have Lava? Because Lava poured in a Crucible allows you to make Obisidan tools. Although their durability is not that great, since Lava can be found quite easily (especially if you open an early Nether Portal) and since Obsidian is a Tier 3, Fire Aspect material, Obisidan tools are the perfect upgrade after Flint ones: plentiful, efficient, and easy to make. Because Lava is hot, pouring a bucket of it in a Crucible will heat it immediately to Lava level (around 1000K) and you'll be able to pour the lava right away in tools shaped molds. That's the beauty of it: you don't even have to heat the Crucible with a Burning Box. For this very reason it's a good idea to find an underground lava lake beneath you base and keep a Crucible + tools molds there. Be careful when pouring because obsidian tools need to cool a bit before they can be safely picked up, or use pincers/hazmat suit when available. Tools retrieved from molds are "raw" and need to be sharpened to be of any use so finish them with a file, or better, a Sharpener. Of course you can use your Tools Molds with other materials, like Bronze. 
- A Thermometer. It's really easy to overheat the crucible without it. You'll need two units of Red Alloy (4 Copper + 1 Redstone = 1 Red Alloy unit). Be careful because Red Alloy burns off most of its mass once it hits its melting point so overheating is very easy. You'll also need some glass, and Tin Alloy which is made from Tin and Wrought Iron. A Thermometer is placed on the front of the Crucible. You'll need a wire cutter, a rolling cylinder and a hammer to turn red alloy plates into red alloy wire. It's a time effort to craft your first thermometer, but it's really worth it: you'll make tremendous progress in understanding the smelting process and in managing your Crucible safely. 
- A Cauldron is made of 7 Iron plates (or Wrought Iron plates so you can use them there if needed). The Cauldron is, with the Sifter and the Hammer, the next step in your ore mining process: throw in crushed ore and impure dust to clean them and get by-products. It's especially worth it to clean crushed ore because otherwise it'll bring a bunch of stone with it into the cauldron. You want to try to smelt washed, purified dusts as much as possible. 
- A Sifter costs 8 units of Steel, but it's your only way to manually process Sand and Gravel Ores, which are in huge veins, so it's well worth it to craft it as soon as possible. Right click Ore onto the top spot to place it there, then hold down right-click to sift the Ore, then, after it has passed through the Sifter, right click the bottom result to pull out the purified Ore and extracts. Crushed, purified gem ores can be sifted to get gems (this includes Lapis). Gravel can be sifted to get Flint, Quartzite and trace Clay. Dirt can be sifted to get pumpkin, wheat and melon seeds. You can wash the Purified Dusts in your Cauldron to retrieve even more byproducts afterwards. 
- A Sharpener costs as much as a Sifter so only consider making one if you've found some Steel or a bunch of Graphite Ores, but the investment will pay off big time because sharpening your raw tools is almost a daily occupation in GregTech since you'll mine a lot and cut down tons of wood for Charcoal. Place your Sharpener on the ground, feed it Sandstone with a right-click in the middle of the Sharpener, and keep right-clicking your raw tools on it. After a few tries your tool heads will be sharpened, preventing you from using a file to do so, which costs time and resources. 
- A Mixer is quite cheap and can go a long way if you're into Bread for food: Harvest your wheat (hint: use a Sense, it'll farm in a 3x3 pattern), grind it into Flour with a Mortar, put the Flour in the Mixer with a right click, and pour water in with a Bucket (Iron or Wood made): right-clicking with an empty hand will get you Dough, that you'll be able to craft in Bread, Baguette, to be then cooked in a regular Furnace, so that you can make Sandwiches! You'll need 1 water unit for 3 flour so place your mixer near a well to spare you water trips. Or you can kill a lot of animals for eating, that works too! 
- A Dust Funnel may cost a bit of Steel but it may quickly become a valuable tool. Like the other contraptions it's GUI-less: you right-click dusts of any size (from blocks to 1/72th pile) and it will output through its bottom whatever dust size you set it to. To change the dust size (default is block size), just use a Monkey Wrench on it and you should see its internal funnel shrink in size until it returns to block size again. It may seems superfluous but once you'll have a steady ore processing facility, you'll enjoy not having to regroup all these dusts of various sizes. 
- The Reinforced Chest is a very good replacemend for your good old double-block chest, because, it has the same capacity, while only occupying one block. This is very interesting when you start to build up you factory and all the machines and pipes start to be all around the place. Plus since you'll unvoluntarily hoard some materials (mainly Silver and Gold) while processing others (Copper for example has Gold as its by-product), you may sool realize that you can spare quite a lot of them in making these convenient chests. 
- An Advanced Crafting Table is all you ever dreamed of the Crafting Table: You can store components in its drawer, and they will automatically fill the blanks in the main crafting grids. You can pipe in fluids. You can keep you tools at hand. You can use blueprints to make your items automatically. And finally you can use automation to provide items and suck out results. It's truly a blessing that come in a lot of different materials, even Lead so you can build it very early in the game! 
- GregTech has its own variation of Hoppers and you're going to love them. Like all other variable metal-based contraptions the material you use has a consequence on the Hopper capacity, but even the most basic one can be of a great help, like feeding a Crucible with a lot of dusts (the crucible can only have up to 16 dusts and any you throw beyond the 16th will just vanish), or extracting hot metal from a Mold, or automatically extract ashes from a Burning Box. Being creative with a Hopper can be very rewarding, alleviating all the boring tasks and letting you focus on fun ones. Note that you can use a Screwdriver to tune a Hopper stack size management. 
- A Bath (not to be confused with a Mixer Table) will help in handling dipping recipes, like Wood Pulp and Water into Paper or Wood Pipes and Creosote Oil into Wood Sealed Pipes. If you need to fill it with a portion of a Bucket , you can use a Measuring Pot. If you want to empty it, you can flush it with a Plunger but remember that its content will simply vanish. 
So, at the end of the Forge Age, your current work process is now: 
- Mine Ores/Collect Sand&Gravel Ores 
- Crush Ores with a hammer, or Sift Sand&Gravel ores with your Sifter 
- Wash results in Cauldron to get by-products 
- Crush Purified Crushed Ores (again) with a Hammer 
- Wash the results again in Cauldron to get even more by-products and purified Dusts to smelt in your Crucible 
Better, isn't it? But a lot of labor work. Why don't we start letting machines do the hard work for us? 

The Steam Age:
Your first machine:
Now that you're more familiar with the Burning Box heating principle we're going to mess with scary, scary steam power. Steam, at this point of the game, is the only way to power your first machines. 
As an explanation, let's make ourselves a Rolling Mill. It's a basic machine that does not require a lot of expensive materials, and building it will help you understand the Steam mechanic in GregTech. Additionnaly, it will be of continuous use throughout your GT Carreer, because it'll allow you to focus on storing ingots (Take a look at Stacks on Stacks, btw) instead of storing ingots and plate. 
Make a lot of Bronze and craft a Bronze Boiler, some bronze small pipes (4/5 should be enough), a Bronze Steam Turbine and, finally a Bronze Rolling Mill. 
Put the Boiler on top of the Burning Box, like the Crucible, and put Water inside by right-clicking water into the front side of the boiler. Then run pipes from its top hole to the back of the Steam Engine. Put the Rolling Mill in front of the Turbine. 
When lit, the Burning Box will heat up the Boiler, just like it did with the Crucible. Water will slowly reach its boiling point and during that time the barometer will rise slowly throughout the left white section up until the green zone: that's the moment when you'll start to have Steam. Steam will flow through pipes and will go inside the Steam Turbine. The Steam Turbine with then use this Steam to make its internal turbine rol, which will generate rotational energy, measured in GregTech as RU/t. 
Rotational energy is then consumed by your brand new Rolling Mill that will turn it into internal energy (measured in GU, always with a 1:1 ratio regardless of energy input type). Put an ingot in the Mill and it should be transformed into a brand new Plate! 
Naturally, being a machine, the Rolling Mill does not wear off. You just have to feed it energy (RU in this case) to make it work. 

The Hazmat Suit:
Now as a more advanced tutorial, let's make ourselves a Hazmat Suit, which is a lot of work to do but will help you understand why Steam is awesome, and the suit itself will be of great use to you. 
Note: If finding the necessary materials for a Coagulator is too much trouble for you, feel free to skip this whole part. The Hazmat Suit is a very nice thing to have, especially when you're not fully familiar with the Crucible, but it's not mandatory in any way. 
Go to the desert and find a Sand Bauxite/Sand Ilmenite vein. Dig up all the Ilmenite, and put it through the Sifter. Ilmenite smelts down to 1/4 its volume in titanium. You can dig up the Bauxite too because its by-product is Aluminium and you'll need a lot of it later, but it's not mandatory at this point. 
Once you've got the required amount of Titanium, Craft a Titanium Burning Box, a Titanium Boiler, a Titanium Steam Engine, and a Bronze squeezer. 
To turn your Latex into usable, solid Rubber, you'll need a pain in the butt Coagulator, made of Stainless Steel. You'll need Iron, Nickel, Chromium (found in dungeon treasure chests or extracted from ruby ore (TOBECONFIRMED)) and Manganese (dungeon treasure chests or extract from grossular/spessartine/pyrolusite/tantalite). Ratio is 5 Iron, 2 Nickel, 1 Chromium, 1 Manganese. You'll need 12 ingots to build the coagulator so you'll have to make 2 batches of 9 Stainless Steel each. First combine Iron and Nickel to make Invar, otherwise the Nickel will get permanently bound with the Chromium to make Kanthal, preventing you from completing the recipe. 
When you have all your machines install them like you did for the Rolling Mill: run the Titanium Pipes from the top of the Titanium Boiler to the back of the Titanium Steam Engine, place the Squeezer in front of it and place the Coagulator under the Squeezer. 
Then feed your Burning Box with Fuel, your Boiler with Water, and your Squeezer with Sticky Resin. Light the Burning Box and wait for the Boiler to heat up to its green zone. After a couple seconds your Titanium Engine will start to move its internal piston back and forth (no animation for the moment, just look at its color changing to green), and your Squeezer will happily squeeze your Sticky Resin into Latex. The Coagulator will then suck up the Latex from the Squeezer, and slowly turn it into rubber bars. Note: a Coagulator does not use any energy, just time. 
Use your newly acquired Rubber, Orange Dye, Wool, Glass and Iron Bars to build a Hazmat Suit and Rubber Shoes. It'll protect you from all crucible accidents and it'll allow you to pick up hot finished metal from molds without pincers. Note: You have to wear the whole set (Head, Chest, Legs AND the Rubber Shoes) for it to work as heat retardant. If only one piece is missing, you lose the effect completely, so be careful when using your Rubber Shoes everywhere. Note also that the Hazmat Suit does not lose durability from using it to get stuff from molds, or even handling radioactive elements. It loses durability just like any other armour pieces: when you take damage. 

Energy Types and Efficienc:
So, to sum up the previous tasks, you used heat (measured in HU/t) to power a Boiler (which converts HU/t to Steam/t) to power a Turbine (which converts Steam/t to RU/t) or an Engine (which converts Steam/t to KU/t) to power a Rolling Mill (which converts RU/t to internal GU/t) or a Squeezer (which converts KU/t into internal GU/t), and in the case of the Squeezer, transferred its content into a Coagulator (which uses Time as a resource, measured in ticks (t), or seconds (1 sec = 20 ticks)). 
There are several more energy types you should be aware of so here's a list of all of them: 
- HU/t is Heat energy. Made from Burning Boxes and Electric Heaters, you already know them for their use with a Crucible and a Burning Box, but HU is used but a lot of very useful machines. 
- KU/t is Kinetic energy. Made by a piston going back and forth, it's the energy required by a Crusher, a Sifter and a Compressor. 
- RU/t is Rotation energy. RU/t is very important because it's used by a lot of basic machines, so having several good RU/t producers is critical. 
- EU/t is Electric energy. Encountered later (during the Electric Age) you may already know EU/t as IC2 Energy system. Well you can just keep your general understanding of the concept and scap anything specific because it changes quite a lot in GregTech. 
- MU/t is Magnetic energy. Generated by Magnets (duh!), it's a less used energy type but don't worry, you'll have to use it at some point too. 
Another point to consider is your machines efficiency, starting by the Burning Box, which is at the very beginning of you chain. As you're read earlier, a Burning Box can be made of several materials, which can then themselves be of basic or dense state. Theses two parameters has a dramatic influence on the Burning Box resulting power, and efficiency. 
For instance a Titanium Burning Box is very powerful (96 HU/t) for something you've built quite early, but it's efficiency is a meager 85%, while an Invar Burning Box, although less powerful (64 HU/t), have an outstanding 100% efficiency. The efficiency means your fuel will last more, and since you'll be burning a lot of fuel, having a perfect efficiency may sometimes be more important than raw heating power. Or course nothing prevents you from using a Burning Box at some point and then replace it for another one, under the same Boiler. 
This efficiency rate is applied to almost all machines, so do not hesitate to do some math to understand what you need, and how you're going to produce the needed energy type and at which rate you're going to produce it. Again, I cannot stress enough the fact that you should read the tooltips again and again. 
If you overlook this two majors things may happen to your engines: they will be underpowered, even so they might not even start, or they will overflow and even explode. You may restrict the flow of Steam your boiler will produce with pipes (look at their tooltip to see their maximum bandwidth) but limiting the flow can have another undesired effect: Steam pressure will build up in your Boiler. If your Boiler go beyond the red zone, it will explode, and the blast radius isn't small. So be careful and think about what you're doing: Read the tooltips, adjust your math accordingly, and play it safe. 
Making a machine may be long process, it would be a shame to waste all these efforts, wouldn't it? 

Calcification:
Calcification is a nasty consequence of boiling natural Water. The water you'll use in the beginning is considered impure. This water, when boiled, will slowly but surely calcify in your Boiler, making it less and less efficient over time: for a given quantity of HU, it will output less and less Steam. 
You can safely check the calcification status of your boiler by using a Magnifying Glass so better craft one as soon as you've found one of its possible glass crystal components. You can make this check at any time, even when your Boiler is running. 
You can decalcify a Boiler by using a Chisel, but only if it has stopped running and its internal pressure has gone down to the white zone, and you better have a Hazmat suit because if it's still hot you may instantly die. 
You can also decalcify a Boiler by removing it with a wrench and put it again on the Burning Box. This is the safest way, but it uses your wrench. 
In both scenarios, decalcifying will empty the Boiler of its content (Steam and Water) so remember to fill it up again with water afterwards. 
To avoid Calcification you have to use Distilled Water instead of regular Water. Making Distilled Water is quite easily, because each Steam consumer engine (Turbine and Engine) emit 80% of its used Steam as distilled water on its sides, so you can plug fluid pipes all around them and collect the generated distilled water in Tanks or Drums (more on that later). There will be many more ways, each one more quick and efficient than the previous, to make Distilled Water later in the game. 

Basic Machines:
Now that you are more confident in getting your items parts from casting liquid metals and alloys into Molds, a word on this topic: You should craft almost all Molds as soon as possible. You're going to make more and more machines which will need more and more machines parts like Gears, Rods, Bolts, Plates, and so on. You'll be able to craft these with Ingots and Tools, but in doing so you'll lose a significant quantity of material in the process: For instance, crafting a Plate (1 unit) means hammering two Ingots (1 unit each) together and hammering the double Ingot to get the Plate. So you "paid" 2 units of material and 2 hammer crafting uses for 1 unit worth of Plate. If you've had a Plate mold you could have directly casted the material as a Plate, costing you only the unit worth of material you've put in your Crucible. 
So think about what you want to make, and prepare your materials manufacturing list in advance: You can make batches of Plates, Rods, Gears to avoid having to craft them afterwards. Only exception are Screws, which will need a Lathe to make instead of casting material in a Mold. 
Now your biggest concern will be what to make next. As always with GregTech the answer is simple: More machines to help us make even more machines! 
Your basic machines will be ones that help you build more machines: 
- Automatic Hammer (KU based, back side): Will crush Ores you manually place in front of it. Be aware that not the material of which the Automatic Hammer is made determines what Ores it can crush. 
- Rolling Bender (RU based, back side): Mainly transforms Plates into Curved Plates and Rods into Springs. Worth having because you'll use your bending cylinder quite quickly when you'll start to make pipes, batteries, and rotors, which require a lot of Curved Plates. 
- Lathe (RU based, back side): Mainly transform Bolts into Screws. Useful because screws have no Mold of their own, and are a rip-off to craft from bolts, cost-wise. It also makes Sticks out of Planks, and in a very fast manner. 
- Shredder (RU based, left AND right side): Transform almost everything into dust, including machines, but no Ores (Crusher will do that). Very useful as a recycler of old, obsolete machines/engines. Can also turn Wheat into Flour and Scraps into Dust. So basically an automatic, next tier Mortar. 
- Mixer (RU based, bottom side): Replaces your table Mixer if you've got one but it's way more efficient since you can feed it water automatically (more on Liquids later) 
- Buzzsaw/Cutter (RU based, back side): A little more tricky to craft because of the Diamond Dust requirement, the Buzzsaw/Cutter is you Saw replacement, and can also turn gem into Plates, so it's a direct dependency to the Crusher (Diamond Plates). It's also a very efficient Planks from Log maker. 
- Sluice (RU based, back side): The Sluice is one of the most rewarding machine because it does the first "Wash in Cauldron" step way better than you could ever do, even with redstone contraptions to fill you Cauldron, and more reliably. You can put a Chest on top of a Sluice, feed it with a ton of Crushed Dusts and go about your business while it safely washes all of your dusts. A Sluice need water from its top spot and produces Sluice Juice you can collect in a Tank/Drum to later Centrifuge it or Dry+Magnet Separate it into other by-products. 
- Centrifuge (RU based, bottom side): The Centrifuge is the last of the basic machines but also the most rewarding one because it does the second "Wash in Cauldron" step way better than you could ever do, even with redstone contraptions to fill you Cauldron, and more reliably. You can put a Chest on top of a Centrifuge, another one on its right, feed it with a ton of Impure Dust and go about your business while it safely takes care of your dusts. The Bronze one will do almost all basic centrifuge recipes, but you may soon realise that a lot of recipes need a more powerful Centrifuge, so a Steel might get appealing then (but it will obviously require a more powerful Turbine). 
Note: Unlike IC2, GT Machine are always running (that is, until you've made some specific Covers for them to not do so), so if you're not using a machine, do not forget to unplug its pipe (use your wrench to "undo" the pipe that enter the machine) from the main Steam supply. You wouldn't want to waste Steam, would you? 
Once you've got the necessary requirements, it's time for your two bad boys: the Crusher and the Sifter. These two will replace the most tedious work you've done until now: crushing ores with your hammers (using a ton of them in the process, and a ton of time to use/make them) and sifting sand/gravel ores (which is just time consuming if you've built the Sifter). Both use KU so your Titanium setup, if you went along the HazMat path (if not better start now) will be of good use here. 
Now your work process may still be not 100% automated, but all the hard work (making machine parts, grinding Ores into purified dusts) should now be handled by machines, leaving you plenty of time to harvest more and more Coal/Charcoal to feed your never ending Burning Boxes. 
But, as usual now, some notes before diving in the next Age. 

Multiblocks Machines:
What's more fun than building machines? Building bigger machines, of course! 
- You'll build a Coke Oven quickly after you have build you first burning box, because it's the only way to get Charcoal out of Wood. The Steel requirement may seem steep but you won't regret it. Plus it produces Creosote Oil and can process Purified Lignite Ore as well as Purified Coal Ore. FYI in terms of fuel power, the ranking is as follow: Lignite (2), Lignite Coke (4), Coal/Charcoal (8) and finally Coal Coke (16). Note that Lignite Coke, although being half as powerful as Coal/Charcoal, can be found in much greater quantity, and the Coke Oven will produce more Creosote Oil out of it. 
- A Distillation Tower will come later, and will be a milestone on its own, but there's nothing like having a giant refinery in your own backyard (MORETOCOME). Of course you can use BC Oil Spring (BuildCraft) in it. 

Liquids and Gasses:
GregTech does not have fluid (liquids/gasses) tanks (yet) so your alternatives are: 
- BuildCraft Tanks: Cheapest of the lot (8 Glass), they are also the less practical because even though they can be filled/emptied with water with a bucket (iron or wood one), and stacked on top of each other to increase overall capacity, you can't move them without losing their contents, and their capacity is minimal (16,000L). You can use them for water-based machines like the Buzzsaw/Cutter/Mixer/Centrifuge/Sluice but you may be quickly frustrated about their drawbacks, though 
- ThermalExpansion Portable Tanks looks like their cousins from BuildCraft but they can be crafted from different materials for more capacity, which is always nice to have. Portable Tanks can be picked up instantly with a wrench, and always retain all of their fluids no matter how they are picked up. They even retain their fluids when upgraded in a crafting table. They also act like BuildCraft Tanks when stacked vertically, effectively adding their capacities together due to the way fluids will automatically move up if they are pumped into a lower tank, or down if they are pumped out of it. Finally, a Portable Tank will automatically output liquid to the block below it when right-clicked with a wrench. 
- EnderIO Fluid Tanks are the most automation-friendly of the bunch. They come in Iron (16,000L) and Dark Steel (32,000L) variants. A Fluid Tank has several item slots that can be used to empty or fill buckets, cells, and other fluid containers. Each side of the tank can be set to output liquids and items to a neighboring block, or pull liquids and items from it. Like Portable Tanks, they retain their fluids when picked up and can be picked up instantly with a wrench. Holding a tank and right-clicking on another fluid container will fill the tank from the container if it empty, or will otherwise empty the tank into the container. Compared to Drums, they can hold much less fluid per unit of metal, but the automation features will easily make up the difference when they are needed. 
- ExtraUtilities Drums are the serious business. They are very expensive (17 units or Iron for ONE drum), but they have a capacity of 256,000 L (256 Buckets), they can be fill/emptied with buckets, removed while holding their content (this is their main benefit) and they also take the color of the fluid it stores. 
You can pipe any BC/GT pipe into these tanks/drums and they will be filled at whatever rate the pipe is made for but extracting fluid from them into GT pipes will require a Pump Cover. Pumps can run without energy (so, for free) so craft yourself a couple ones, you won't regret it, especially when you'll start juggling Drums to tranform Water into Distilled Water or Sluice Juice, and then use these fluids for another tasks later. Just put a cover on a pipe, adjust its flow direction with a Screwdriver if necessary and it will suck up the fluid from a Tank/Drum and inject it into the pipe. 
Of course you can pipe machines input/output fluid spots with fluid pipes. For instance you can pipe the fluid output of a Sluice into the fluid input of a Centrifuge, like you did (without a pipe though) when you put the Coagulator under the Squeezer. Likewise you can plug Item pipes in and out of machines to carry your items automatically from/into chests or other machines. 
You can also just put a Tank/Drum just next to a machine's fluid input/output and the machine will suck/export the fluid with it. Note: It may take a little bit of time for the machine to actually "detect" the Tank/Drum. 
One more note, this time specifically on Gasses: you can use wood pipes for Steam as starters, but they won't be hermetic, so hot gasses will leak and in doing so will damage you if you don't have a Hazmat Suit. So be carful around using them, and consider making sealant as soon as possible, or switch to metal fluid pipes, like Copper or Bronze. 

Machines Chains:
You surely have guessed it by now, but one of the prevalent aspect of GT is production chains. Machines are your basic components that you compose in several combinations, each one more and more complex, to easily and reliably achieve your goals in automation. 
To inspire you, and to introduce some of the lesser known (but not so less useful) machines here are a Production Chain list you can set your mind to: 
- Machine Parts factory: Rolling Mill/Rolling Bender/Cutter/Lathe. You input Ingots and you end up with Plates, Curved Plates, Springs, Rods, Screws, and so on. A good one to start with because you'll use it to make all the other chains, obviously. 
- Ore Processing Plant: Crusher/Sifter => Mixer => Shredder => Centrifuge. You input Ores blocks and end up with Pure Dusts, a lot of by-products (and pretty Stone Dust for your walkways), and Sluice Juice. Beware the requirements on some machines though. 
- Bread Mill: Shredder => Mixer => Furnace/Smelter. You input Wheat and get Bread Dough, that you can then cook to make Bread, and then Sandwiches! 
- BioEthanol Rig: Shredder => Fermenter => Distillery. You input plants (Saplings, Logs, ...) and you get Ethanol and Distilled Water. Ethanol can then go in a Liquid Burning Box as fuel, while the Distilled Water can very efficiently replace regular Water in your Boiler. 
- Saw Mill: Buzzsaw => Lathe. The simplest, but oh so rewarding of them all after wasting so many saws...You give it Logs, it gives back Planks and Sticks with a best-than-vanilla ratio. 
Of course in the beginning you will struggle to make a chain, having to switch machines between your few engines/turbines but slowly but surely, if you keep some clear production chain goals, you will see the results, and yearn for more! 

The Electric Age:
Steam may still be your main power production for a while but at some point you'll start to feel the need to store all this energy, maybe to use later at a much higher rate, or just because you have a fuel excess you are already burning anyway. You may also be interested in other energy types like MU, renewable energy, or just want higher tier, more efficient and powerful machines. 
For all these needs, at some point you'll have to step up to the Electric Age. 
The Electric Age is not a whole different Age than the Steam one. Actually in the beginning you will use a lot of Steam to create your Electricity. So don't scrap away your beautiful, intricate, set of pipes and engines. You're going to use these almost the same way, to power up batteries. These batteries will then power electric machines, which are much more efficient than the Steam ones. 
Your starting batteries are made of Battery Alloy. Made from Lead and Antimony (following a 4:1=5 ratio), Battery Alloy will allow you to build Battery Hulls, these hulls with be filled with various substances that can chemically store Electricity. The very basic one is Redstone, but more are to come, like Electrotine or Teslatite. 
Charging your batteries means first creating electricity, and for that you'll be needing a Steam Turbine and a Dynamo. The Turbine produces RU and this energy is consumed by the Dynamo to make EU, just like you bike uses a dynamo on your bicycle wheel to generate electricity, and thus light, when you're riding it. 
So plug a Steam Turbine, a Dynamo and a Battery Charger in a chain and put Redstone Batteries in there. They will slowly charge up as the Turbine recieve Steam. The materials involved has a lot of impact of the Steam requirements and the generated EU, so, like with the basic machines, be careful when you're crunching your numbers to decide what to build and read all the tooltips. 
Then you can start making advanced machine explode by using improper Voltage or Amperage... 
(WARNING, EXPERIMENTAL ZONE. I may write a lot more absurdities than usual because I just reached this part, feel free to correct me) 
The two main aspect of Electricity, Voltage and Amperage, are modeled in GT6. This means that instead of following a simple Tier system, where you just have to make sure the numbers of two tooltips match (32EU/t in a wire, 32EU/t in a machine), GT allows you to feed a variable amount of electricity in your machines, so that you can slightly underpower or slightly overpower a machine, like you did with Steam albeit sometimes involuntarily because of Boiler calcification. Of course, a too big deviation will result either in a non-running machine or an exploded one, so again, be careful, plan ahead and use a calculator. 
Electric Machines and Wires, are defined by their ability to support Voltage, and their ability to take in Amperage. The product of the two is Power (like you have learned -or will learn- in High School). As long as you're careful with these two values, everything should be fine. 
Amperage is defined by the number of batteries you use at once in the battery charger. 1 battery means an Amperage of 1, 2 means an Amperage of 2, and so on. So you can tune your Amperage in real time if needed. 
Voltage is more like the EU tier you are used to. Machines need to support the circuit Voltage to be able to let the Amperage work its magic inside them. Voltage is also your basic tier converter with IC2 setup, so you can use a Polarizer/Magnetizer combo with Tin Cable powered by a Battery Box, for instance. 
When you have a solid Electric charging setup, you should consider walking the long path toward Solar Panels, because renewable energy alleviate the need for fuel for your batteries, and mostly because it'll require a lot of thinking, craftings, and general GT machine usage to do so. Nuclear Energy can then be considered too, but of course be careful around radioactivity, and the blast radius. 
And then you have Electric tools, Laser technology, the Robotic Age, and so many other things not covered in here that will help you automate more and more steps in more and more complex work process and productions chains... 
One final word: GT6 is in continuous developement so feel free to check in regularly to see everything new. 
And, as always, good minin' and good craftin'! 