Yeah, go to any jeweler, or even Target or Wal-Mart. There is a liquid jewelry cleaner you can buy for like $5. You insert your jewelry for about 15 seconds, brush, rinse, and you are good to go. I actually did that this morning.

There are also cloths, but the liquid cleaner is so much easier, quicker, and not as messy as the cloth. With the cloth, the dirt from the jewelry will stay on the cloth and get on your hands every time you use the cloth. You don't want black hands.