Crafting allows you to take materials obtained while hunting and use them to create new equipment or upgrade equipment you already have. Crafting costs shells in addition to the items listed by the forger.
Once everything needed for the crafting process is acquired, equipment can be created at a either a
Weapon Forger or Armor Forger. Crafting is tied to the level of the character, and the the forger will always successfully create your item if you have all the required ingredients and can pay the cost.
Materials can be found by killing beasts in the Hunting Grounds or by gathering them from Collection Sites. Certain items may also require other pieces of equipment. Using the forgers to upgrade items creates a more powerful item than the one you started with. Press the arrow on the bottom of the right hand vertical menu to bring up the Weapon/Armor Tracker. Here you can get more information on which materials are needed to create the item. Note that the Weapon/Armor Tracker can't create the item, for that you need the Forgers who can be found in Zones 1 and 2.
Higher ranked materials have a better chance of dropping in harder hunts, with Challenge netting the most