Inna,
The simplest and, to my mind, safest method is:
Use an aluminum pie plate or a pyrex dish with a sheet of aluminum
foil in the bottom. Add very hot (almost boiling water). Lay your
jewelry so that it’s on the aluminum part of the surface. Sprinkle in
baking soda (liberally). Allow to bubble away. Rinse and repeat if
necessary.
The chemical reaction that takes place is like a battery. It removes
the oxides (tarnish) and smells a little sulphury as it’s bubbling
away.
For chains and liquid silver, you can also make a thin paste of
baking soda and water and rub it gently onto the piece with your
hands. Allow to soak and then add it to the aluminum tray with the
very hot water.
Hope this helps!
Karen Goeller