Melee attack. Press three times in quick succession to do a short combo. Hold the button when moving while your Stand is off to do a charge attack that knocks enemies down.
Dodge. Most characters will do a roll, though some may dodge in a different manner.
Special move. These vary between characters.
Pauses the game.
Toggles your Stand. Pressing the button while your Stand's off will turn it on, and vice-versa.
Stand Shoot. This will usually have your Stand come out and do a quick attack. For most characters, holding then releasing the button while your Stand is on will perform a longer, more damaging attack.