I can't speak specifically for Warrior, but for both PLD and DRG AF that I have done so far, you get them as you complete your Job quests. Paladin I got by heading to 4 different areas, each with a coffer and some enemies to kill. Dragoon I got from completing some trials that were set (I believe - I already had the AF from 1.0 so it never actually showed up to collect).

I expect something similar exists (some challenge to overcome) for the other Jobs. The final AF piece, the body, is gained from the final quest along with your final ability (again, I believe).