It doesn’t look pretty in your jewelry box, but THE EASIEST WAY TO PREVENT TARNISH IS TO KEEP YOUR JEWELRY IN ZIPLOCK BAGGIES. No, we are not kidding. It works on silver or gold vermeil (gold plated silver), because air causes tarnish. Baggies isolate the jewelry from air - Go Baggies! Also, anti-tarnish strips also work for about six months. (Hence, all jewelry from LP comes in little baggies with anti-tarnish strips).
So what to do when its already tarnished?
For light tarnish, you can use a treated polishing cloth (aka, rouge cloth, silver cloth). It takes a little rubbing, but the chemicals embedded in the are relatively gentle, but effective - the polish will last a long time. I like the ones with two attached cloths - an inner, chemically treated one and an outer one for buffing.
For heavy tarnish, there are a couple of options:
You can use a dip (e.g. Tarnex) which is available in most grocery stores - a fast option, but be aware that dips contain corrosive chemicals, and that some are metal specific - make sure to wash your jewelry before and after, and read the fine print before you dip!
For a more gentle, but labor intensive option, you can use a polish, such as Goddard’s or Wright’s. Just get some rags, stick in a DVD so you dont get bored, and follow the instructions on the back of the can.
Finally, there is the electrochemical method we learned in seventh grade. Get a cheepo aluminum pan, pour baking soda into the corners, put your silver in it, pour boiling water on top, and let it sit there for a few minutes. The baking soda transfers the oxidization to the aluminum, so throw the aluminum out after. You can also use a glass dish lined with aluminum foil.Take it out, RINSE IT OFF and buff it with a polishing cloth.
Finally, be very gentle on matte finishes and don’t polish silver thats been intentionally oxidized, like these earrings. You will lose all that pretty depth.
When in doubt, polish gently. Oxidization gives pieces dimension.