My first play through. I am on level eight and in this room where it says exchange keys for gems. I don't know how to get out or how to proceed through the game. If you need more details, just ask. Thanks

Take a jeweled key put it in the cubby, push the button, take the jewel, put it in the socket by the door to open it. Also turn 180 from that wall and throw something at the writing across the way.

If you have neither gems nor jeweled keys you haven't explored enough. Remember there's a cluebook included with the games, just open the .pdf from the menu in Galaxy, or look in your library for the file.