Actually, I spent yesterday cleaning my silver jewelry…with SCIENCE! Bear with me, the pictures are still from my cellphone.
First, you line a small pot with aluminum foil. Throw a couple of tablespoons of baking soda in, fill the pot with about an inch of water (or however deep you need to cover your jewelry.) Bring it to a boil.

Bubble, bubble, toil and trouble...
I tried to take a picture of my silver so you could see how dirty it was. This was the best picture I could get.

Dirty, tarnished, silver
Once the water is boiling, take it off the heat and drop your jewelry in.

Tarnished silver in the pot, nine days old... Um. Sorry.
It works very well. Apparently tarnish is made up of sulfur (which you will smell) and sulfur likes to bond with aluminum more than it likes to bond with silver. Something like that anyway. All I know is my silver is nice and clean and I didn’t have to try and polish in those little tiny crevices.

Voila!
So here’s the best part of this cleaning method. It’s all stuff you have in your own home. It’s so easy even a lazy cook can do it. And you don’t have to use commercial silver cleaner (seriously toxic stuff). You will, however, need to rinse your jewelry unless you like wearing gritty earrings.