There are two methods to acquiring Zero Suit Samus. The first and easiest method is to hold down the R button (on the GameCube or Classic controllers) or the B button (on the Wiimote) from the stage select screen. Hold down R, select Samus, select your stage, and then release the R button. You should start the battle not as "armored" Samus, but Zero Suit Samus.

The other method is if you decide to start the battle as regular Samus. You can switch to Zero Suit Samus by quickly pressing up and down repeatedly extremely fast on the d-pad. This is difficult to do, and can't be done on the Wiimote (since the A button only provides one taunt, and there's no other equivalent). If you do this, keep in mind that you can't switch back during the battle to regular "armored" Samus.