Note: If you have silver items that have oxidized details (black background with raised polished accents), or sayings stamped into your metal, this technique may remove that background contrast. If you just want the raised area cleaned, use a polishing cloth.
All you need are:
* Plastic dish (big enough to dunk your silver pieces. I use a tupperware dish)
* Aluminum foil
* Baking soda
* Hot water
1) Put a piece of the aluminum foil at the bottom of your dish. Place your silver pieces so they are in contact with the foil.
2) Put a few tablespoons of baking soda in the dish.
4) The mixture of baking soda, hot water, and aluminum foil will cause a bubbling/foaming chemical reaction. Swirl your items in the mixture or let soak for tougher tarnish. I took a video of this process here (look closely and see the silver brighten as the water clears at about :30 seconds in!):
5) Voila! You may even smell a little sulphur "rotten egg" smell as the reaction takes place. Rinse and the silver pieces should be clean and shiny once again! If heavily tarnished, try a few additional applications of soda and hot water, or maybe a fresh piece of foil.
What's happening? It's a basic chemical reaction that binds the aluminum to the sulfur oxides (you might see yellow flakes at the bottom of the dish) that the heat and contact with the aluminum foil accelerate. For all the cool science-y details, click here.
The chem-E in me loves it. Works great on chains. If you want to clean silver jewelry with stones or pearls, definitely keep the stones/pearls out of the water (the heat may change color, take away shine, or crack your gems!).
Handmade Jewelry by Peggy Li