Heat some water, add in some baking soda as a catylyst, and drop in a piece of aluminum foil. Probably best done in a glass or ceramic pot.
Touch your silver to the aluminum foil and watch.
The tarnish (sivler sulfide) reacts with the aluminum, the aluminum having a greater affinity for the sulfur atoms, pulls it from the silver sulfide, leaving pure silver and aluminum sulfide.
Note: The silver has to TOUCH the aluminum foil, theres a bit of current flowing there that completes the reaction.
I miss Mr Wizard...