You get AP by doing battles. At the end of a battle on the list of items you got from that mission it will show you how much AP each character in that battle or dispatch got.
Different from the conventional Final fantasy games. It uses a battle system not unlike that of Tactics Ogre and it's more strategy based than the other Final Fantasies. It's storyline is also...
Incidently, yes you can. He can be in your party, and comes with a special job. However, he is level 1 (regardless of your party's level) and needs to be trained a lot before he is any use.