Well to start with the basics there are two types of crafting,
Basic Craft, for which you use special recipies called formula cards to make small things like potions, it tends to get expensive to start off, so I reccomend you avoid this craft. Since a lot of money goes in to formula cards, but not much comes out.
Professional Craft is broken down further into 5 more categories, ranging from swords to armor. You chose which of the 5 you'll get at lvl 50, and once you've decided it can't be changed.
To use a craft you must go to your character screen (c) and select the craft you wish to do. For professional craft you can select what type of item you wish to make and then see a list of different kinds, if you click these you'll see a preview of the item and all the materials you'll need to make it.
Cores - obtained by breaking a similar type of item, ex. aramid cores are obtained by using the core transmuter on any aramid armor.
Lvl 1 Disks - can be bought from the Port Lux Core Alchemist
Lvl 1 Cartridges - bought from the GD, BI, and DS Core Alchemists
Finally you'll need a base item for your crafting, however it's not always what it seems, so scroll over it and make sure it isn't demanding a 2% SWORD amp or a slotted version of the item
