This trick works like magic and kids love it.

Aluminum foil
Baking soda
Salt
Very hot water (can be boiling if you like)
Combine the above ingredients in a clean kitchen sink. Put your tarnished silver and silver-plated items into the sink and let set for a few minutes. Watch as the tarnish disappears from the silverware and reappears on the foil. This is a natural chemical reaction, and a great way to teach the kids some science!

Note: This trick works so well that it will clean out the nooks and crannies that give some silverware the "aged" look, so you may only want to do this occasionally.