Outside of battle:
A - Talk/menu confirm
B - Menu back
Y - Assault (a first strike out-of-battle attack, only usable in areas with enemies)
X - Menu
L/R - Camera rotate (world map only)
Select - View skit when prompted
Touch screen: Tap arrows to cycle between info screens
In battle:
Control pad - Move, up = jump, double-tap backwards = backstep
A - Basic attacks (control pad neutral, up, down, left/right produce different attacks)
B - Devic Artes (as assigned to different control pad directions)
Y - Block, while holding Y back = backstep, forward = dash (through enemies), down = spell guard (consumes TP)
X - Menu
L - Change controlled character
R (tap) - Change targeted enemy
R (hold) - Free run (control pad up/down change to movement)