Hit the other guy. Preferably more than he hits you.
Modern SF games are very complex - you've got your basic attacks (light, medium and heavy punches and the same for kicks). On the arcade that's configured to two rows of buttons; on the 360 I tend to set light and heavy to the face buttons and medium to the triggers, but see what suits you best.
These are modified by pushing in a direction; eg down + heavy kick might give you a crouching spin kick etc. So far so similar to IK+.
Combinations of buttons will give you different attacks; eg towards and hk + hp will result in a throw or grab (though this may be different, I've not played this specific version). You can usually bind these to different buttons if you want, so one of the triggers = hk + hp.
Then you have the specials, unique to each character. Chun Li should do her laser foot kick (I forget the name) if you tap one of the kick buttons quickly. Hold down to power up then press up + k to get the spinning bird kick (though again I've a feeling this might've changed).
Ryu for example has "sweep" specials - press down on the joypad, then sweep around it a quarter circle towards and p to get a fireball. Sweep away with a k for the hurricane kick. down forward down-forward p for a dragon punch.
Then you have the super moves, which you need to power up for - Ryu used to do a super fireball I think, which is two sweeps towards with p.
Then you get into combos and it starts getting really complex...