How do you unlock peach and play her in Super Mario 64?

You have to either beat the final bowser or get every power star

You cannot be Peach in Super Mario 64 or Super Mario 64 DS.

Unless, you have Project 64 or an AR (Action Replay).

Project 64 lets you play Nintendo 64 games on your computer

and it comes with cheats.

An AR is hard to explain.