Here are some ways to clean your jewelry at home.
I have used of all of these & they really work.

1. The quickest & easiest way that I have found to clean my jewelry at home is to use the sterling silver jewelry cleaner that wal-mart sells for $4 dollars. This works great on my sterling silver jewelry that has mild tarnishing. (NOTE do not put jewelry with gem stones in to any mild or strong cleaner because it may damage some stones, this would ruin a peal fast!)

2. Another quick way to clean your jewelry but I do not recommend it because it has strong chemicals is Tarnex. If your jewelry is very tarnished (black) Tarnex will clean it. (Only use Tarnex on jewelry that is not plated. Never put jewelry with gem stones in Tarnex it will make you cry)

3. For sterling silver jewelry with gem stones , I would recommend whitening tooth past. It will take a little work but this is one of the safest ways to clean your jewelry. Get the tooth past very bubbly with a old tooth brush then leave the tooth past on your tarnished jewelry for about 5mins (some times more if very tarnished). After 5mins brush your jewelry till the shine shines through. Rinse with warm water & towel dry. (repeat is you need to) This works great for most of my sterling silver jewelry, it also works great on gold & diamonds.

4. A sterling silver cleaning cloth is the best way I have found to clean my sterling silver jewelry. It will really bring out the shine in your tarnished sterling silver. (also works great on gold). I forget what name brand the one I have is but I know of a site that sells them.
(this takes more time but it is well worth it)
http://www.firemountaingems.com/details.asp?PN=H203075TL

I hope this helps to answer your question.

One more note do not put Antiqued jewelry in 1 or 2. I had a pretty cleric antiqued ring that now looks totally new because I cleaned it with the wal-mart cleaner. If you want your Antiqued sterling silver to be clean but still look antiqued clean it with a cleaning cloth because you are more in control how much tarnish you remove.