I knew you could do it as I remember doing it, a quick two second search brought me to this site. Here's the page from the manual thanks to this site(
http://www.world-of-nintendo.com/manuals/super_nes/super_mario_all-stars.shtml):
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HOW TO PLAY SUPER MARIO ALL-STARS
After you insert the Game Pak in your Super Nintendo Entertainment
System, turn the power ON. After the title screen appears, press the
START Button to go to the Game Select screen. Then use the + Control
Pad to choose a game. (picture of the title screen)
(picture of the game select screen)
After pressing the START Button to begin, you can choose from any of the four
battery-backed game save files. The files marked as "NEW" are ones that have
not been used yet. After you have chosen the desired file, press the START
Button to play the game.
(picture of the file choosing screen)
Pressing the X or Y Buttons on the file screen will take you back to the Game
Select screen. To erase a file, choose it and press the A Button. You can
also change the controller button configuration by pressing the SELECT Button.