Get out a tube of white toothpaste. Dampen your piece of silver with water. Using your finger, a sponge or a soft toothbrush, rub the toothpaste onto the silver. Rinse off with warm water, and dry well with a cloth.
Make a paste of baking soda and water to clean bigger silver pieces. Follow the directions for using the toothpaste. If the silver is very tarnished, leave the mixture on for 20 to 30 minutes before rinsing.
Soak badly tarnished silver pieces in a solution of baking soda and water (about a teaspoon of baking soda for each cup of water). Let sit for 5 to 10 minutes, rinse and dry.
Heat things up for maximum effectiveness. Simmer water or use very hot tap water. Add baking soda and a piece of aluminum foil. Put in your silver pieces, let sit, rinse and dry.