Choose Amy, then go to Zone 1 Act 1. Go to the spring that is in front of the first loop. Stand in front of the spring, then do the Hammer Jump. If done correctly, you should go very high.
Beat the game with any character to unlock the Chao Garden.
Beat the game with all 7 Chaos emerald's and play Sonic's X-Zone. After you defeat him, you will unlock the moon zone.