How do you craft armor in Final Fantasy XIV?

I suggest you do the local leve quests for your craft. The quest provides you with all the needed materials and by the time you finish, you will have a good understanding of how crafting works. Just accept a local leve that is lvl 1. Start synthesis and click requested button on the synthesis menu. Then select your leve quest and commence.

Get yourself a whethered doming hammer, then do as Jon suggested. Doming hammer is the primary Armorworker's tool. Check out http://www.eorzeapedia.com 's wiki for a good breakdown of recipies.