When you have beaten the game once with any character you will obtain the Closet Key which will enable you to change costumes.

Chris Redfield's The Mexican Costume
Complete the game once with Chris on any difficulty setting.

Rebecca Chambers The Mexican Costume
Complete the game once with Chris on any difficulty setting.

Jill Valentine's Sarah Connor Costume
Complete the game once with Jill on any difficulty setting.

Chris Redfield's Code Veronica Costume
Complete the game 2 times with Chris on any difficulty setting.

Jill Valentine's Resident Evil 3 Costume
Complete the game 2 times with Jill on any difficulty setting.