1. If you do not have silver polish, you can improvise with toothpaste (just make sure it is not the gel kind).
Dip a piece of silver in water, then squeeze about a teaspoon of toothpaste on it. Rub it with your fingers to make a foam, then rinse off the toothpaste and tarnish. Be careful not to rub too hard or you could scratch the silver.
2. Make your own silver cleaning paste. Start with a couple of tablespoons of baking soda and just add enough water to make the paste. Spread the paste on the silver and let it sit for 10 minutes. Then rub the paste gently into the surface of the silver and finish up by rinsing with clear water. Dry each piece with a soft cloth.
3. You can also polish silverware with milk that has gone sour. Soak the silver in milk for 30 minutes to loosen the tarnish. then wash in warm soapy water. The pieces will shine like new.
4. Another approach to removing tarnish from silver is called ion exchange - a process that, despite the fancy chemical name, uses nothing more sophisticated than aluminum foil.
Just line a pan with the aluminum foil, fill with cold water and add 2 T. salt. Drop tarnished pieces of silver into the water for 2-3 minutes then remove them and rinse off the tarnish.