Crafting the Parts
You must first start off by crafting a Blank Pattern, and turning it into the desired part of a tool on the Stencil Table. You will end up with a pattern specific to whichever part you are going to craft.
To determine which parts a given tool will require, check the Tool Station. Clicking on the desired tool on the left will show which parts it requires on the right side. (Basic tools require 2 or 3 parts; advanced tools require 4 parts, and a Tool Forge.)
With this pattern, head over to the Part Builder (It is recommended to have a pattern chest beside your Part Builder, as you can view the patterns inside the chest from the Part Builder's GUI.)
Note: Even if you're going for metallic tools, you'll need to do this next step anyway.
Make the part from something cheap. Preferably cobblestone or wood, but whatever material you don't care about using up is fine. Place the pattern in one of the left two slots, and your desired non-metallic material beside it on the right. The specifics pertaining to the material you have will show up beside it, detailing its durability, durability modifier, mining speed, mining level, and base attack values. Currently the two right side material slots (although different icons) result in the same outcome. Useful for comparing materials though.
Each pattern has a different material cost, which is shown in the subtext when you hover your mouse over it. This is how many material items it takes to craft. Ex: A tool binding has a 0.5 material cost. Crafting it will use up 1 cobblestone, and leave you with 0.5 of a cobblestone in the Part Builder, whereas a tough tool rod has a cost of 3, and will consume 3 cobblestone to craft. You cannot use the Part Builder to craft with a different material if there's still "half" of an item in it. Remove the "shard" item that's still there, or craft another part that has a cost of 0.5.
What do you do with the shards? You can make another 0.5-material-cost item by using the shard just as you would a full piece of material. If you have enough shards, you can even make a higher-cost part.
Metallic PartsFor metallic materials, you will need to craft a fully functional Smeltery, and a Casting Table.
With your Smeltery set up, and a Casting Table beneath the Seared Faucet, you either need some Aluminum Brass or Gold in your smeltery to make parts. Aluminum Brass is made by melting Aluminum and Copper, in a 3:1 ratio. Every 3 Aluminum and 1 Copper will produce 4 ingots worth of Aluminum Brass.
Once you have some Aluminum Brass or Gold in your Smeltery (you need at least 1 ingot's worth), place the part you crafted earlier on the Casting Table. Then right-click on the Faucet to pour out a Cast of your part. This Cast will be used for all the metallic materials, so don't just throw it away after use.
To cast your new metallic part, place the Cast you poured onto an empty Casting Table. Melt down your metal in the Smeltery, then right click on the Faucet to pour it out over your cast. Keep in mind that your Cast has a material cost, the same as Patterns. A Cast with a cost of 3, will require 3 ingots worth of metal in the Smeltery. It will still pour out if you don't have enough metal for the part. If this happens, you will either have to finish the part by melting more of the same material, pump it out using fluid pipes from another mod, or you'll need to break the Casting Table and lose the material. If you end up with more than one molten material in your Smeltery at once, it will attempt to pour out the bottom one first. Merely click on the metal you want to drain from the control block menu and it will assign that metal to the bottom.
Note: Aluminum Brass, Tin, and Aluminum cannot be used to make tool parts.
Crafting the Tool
Once you have the parts required to craft your item, head over to the Tool Station. Select the item you wish to craft on the left, and put your items into the appropriate slots. The name of the part you will be making will show up on the right if you've done it correctly, and will show its durability, and other stats (dependent on the materials you made your parts out of). If you wish, you can name your tool in the dialogue box at the top of the Tool Station's GUI. The effect is only visual.