In Command Battle mode, all the movement and actual attacks are handled by the AI, but what they decide to do is based on what command you've selected.
Attack -> your character will execute brave attacks at any given opportunity
Death Blow/Special -> your character will execute HP attacks at any given opportunity
Guard -> the character will hover around the enemy and attempt to guard attacks, possibly countering
Summon -> summons manual summons
EX Core -> the character will head towards an EX core
Weapon/Job/Trance/etc -> the character will go into EX mode
Holding L&R will make your character run away and evade attacks. While in an air chase you get options to attack, deathblow and dodge.
Characters will only do the action that's currently selected, and if you don't select a new command they'll just keep going with whatever you said before (so you don't have to keep selecting brave attacks, just hit it once and they'll do it over and over).