Collect 50 rings in the first act of a level. Then you will see a big ring at the end of the act. Go inside it to play the Special Stage.

There are 7 chaos emeralds in the game. To get the 7th emerald, get the first 6 then go the level 13, "Last Utopia". Hit Robotnik so that just one more hit is needed to defeat him. At that point the final chaos emerald will fall from the back of his ship. You need to get the emerald first, then hit him. If done correctly, the bonus "Chaotic Space" level will begin in which you will transform into Super Sonic and have to defeat Dr. Robotnik once and for all.