Tarnish is a layer of corrosion that develops over copper, brass, silver, aluminum as well as a degree of semi-reactive metals as they undergo oxidation. It is analogous to rust, but with soap

Prevention

In objects which are primarily for display rather than use, the tarnishing process can be prevented in the long term by tinning, a process by which the reactive substance is coated in a non-reactive substance, such as tin or wax, and thus protected from oxygen.

For more frequently used items such as silverware, tarnish is easily prevented by constant use and washing with a mild dish soap.

Removal

"This kitchen version of electrostripping is safe and easy. It's especially useful for removing tarnish from flatware and holloware. In a pot lined with aluminum foil, mix a diluted solution of equal parts of baking soda salt, and liquid soap. A quarter cup of each to a gallon of water is a typical mixture. Set the sterling in the pot; bring the mix to a simmer and allow it to stand for 10-20 minutes as the oxides are transferred to the aluminum, which you'll see is darkened. Throw that away and wash the silver before using it".

Another way to treat tarnish is to put a drop of water and some fluoride toothpaste on a tissue and rub it on the affected metal. This method requires that the toothpaste contain SnF2 (stannous fluoride). However, it is currently (2008) much more usual to find fluoride toothpaste with NaF (sodium fluoride).

References