This is called the "Ion Exchange" its a molecular reaction in which aluminum acts as a catalyst. All you do is line a pan w/ a sheet of foil, fill it w/cold water and add 2 teaspoons of salt. Drop your tarnished silver into the solution and let it sit for two or three minutes, then rinse off and dry w/ a soft cotton cloth.
Another trick is gently scrub it w/a soft brush dipped in a bit of ammonia, and wipe w/cloth.
Hope this helped good luck!
Once clean you can pervent tarnish by wrapping your silver tightly w cellophane wrap and squeez out as much air as possable- then wrap in foil and seal ends.