It's essentially a rhythm game. You press four buttons to perform an action but you have to time each button press or else you won't perform the action. For example: Pressing square-square-square-circle will command your patapons to move forward. Pressing circle-circle-circle-square will command your patapons to attack. However, there may be times where you want to purposely drop you rhythm because the movements of the enemies may be out of sync with your rhythm but that doesn't occur too often.
With each successful four button input, your FEVER meter rises. A perfect four button input will grant you more fever meter. When your fever meter is full, you will enter FEVER mode whereby your Patapons will be able to cover farther distances, have higher damage output, have higher defense when performing the defense song and several other perks. However, you will drop out of FEVER mode if your performance is sloppy.
That just about covers the basics. I believe there are demos available for the game so it wouldn't hurt to try it out.