Basic controls
Each of the attacks do different attacks depending on short range and long range. Also, the priority on the attacks varies.
Occasionally the hard punch/kick attacks are double attacks from a distance, and single attacks from far away. As a general rule, the single attacks are easier to link into combos.
Dodge/roll (X+A)
In advanced mode, you roll. In extra mode you dodge. You can hit while you are dodged, which is a free counter hit if you are in range, but it also leaves you open if you aren't. It is a fairly weak attack also. If you roll out of an attack during its execution, you lose one special attack. (The dots next to the meter represent the number of special attacks you have) Rolling has the advantage in that you can roll in range while dodging and attack.
jumping
besides the normal up-forward, up, and up-backward motions on the controller to jump, there are other controls for jumping. Two quick back motions on the controller does a hop backward. also, if you hold down before jumping diagonally, you travel further than normal. Back jumps are autoblock high. That means that you can still be swept. The b-b jump is useful for getting out of throws. Most throws cannot be executed on in-air opponents. (Daimon is the notable exception, though there may be more)
counter hit(Y+B)
After you block a move, you can use this counter hit to strike back and disrupt the rest of the opponent's combo. This requires good timing, and it may be easier just to block the opponent. I don't use this much, but if you do, tell me about it (email)