The best way to clean silver is by reversing the tarnishing reaction, and making the silver shiny again. To do this, you will need:
a pan or dish large enough to completely immerse the
aluminum foil to cover the bottom of the pan...
enough boiling water to fill the pan...
baking soda, about 1 cup / gallon of water
Line the bottom of the pan with aluminum foil. Set the silver object on top of the aluminum foil. Make sure the silver touches the aluminum.
Add about one cup of baking soda for each gallon of boiling water.
Pour the hot baking soda and water mixture into the pan, and completely cover the silver.
Almost immediately, the tarnish will begin to disappear. If the silver is only lightly tarnished, all of the tarnish will disappear within several minutes. If the silver is badly tarnished, you may need give the silver several treatments to remove all of the tarnish.
If you use a polish, some silver is removed. With the aluminum foil method, the silver remains in place. Polishes that contain an abrasive, shine the silver by rubbing off the silver sulfide and some of the silver along with it and can scratch the surface.