In Marvel vs. Capcom 3: Fate of Two Worlds for the PS3 and Xbox 360, each character can have up to four alternate costumes to choose from. You access their alternate costumes by pressing a certain button on the character select screen.
On the PS3 hit Triangle, Square, X, or R1 to choose alternate costumes on the character select screen.
On the Xbox 360 hit Y, A, X, or RB to choose alternate costumes on the character select screen.