How do you upgrade your job classes in Final Fantasy Tactics Advance?

Answer 1

You upgrade your job classes by equipping weapons and mastering different abilities. Once you have the required amount of A-abilities for a particular job you may upgrade to a more advanced job.

eg. To become a ninja you need two thief abilities. If you master all abilities in a job (not just A-Abilities), your character will have a gold star above their head in the job section of the menu.

Answer 2

You have to travel to the Citadel of trials to obtain the Rat's tail. Then you must travel to Dragon Cave and speak with Bahamut. He will grant you your class upgrade then. This requires the airship though.

Answer 3

Use a promotion item, (Hero Crest, Knight Crest, etc.,) on a unit that is level 10 or higher. It is recommended that a unit be upgraded at level 20, or they will lose stats.

For some of the main characters they promote at a certain point in the game.

From path of radiance and radiant dawn, most characters promote when they reach level 21