Using a chemically-treated polishing cloth, gently rub one side of your item at a time.
If using dips and creams like Brasso or Tarn-X, follow the instructions closely. This generally involves applying the solution to your silver then rubbing off with a cloth or soft bristle brush. These products are usually pretty toxic, so if you’re sensitive to chemicals be aware.
An advanced method for removing tarnish from silver is to boil 1 cup of water, add 1 tablespoon of baking soda, a piece of aluminum foil, 1/2 cup of vinegar, and your silver jewelry. Bring to a rolling boil, and you’ll literally watch the tarnish disappear—the chemical reaction pulls the tarnish off your jewelry and onto the aluminum foil.
Keep your jewelry in a soft cloth bag or in a sealed box. Air is the enemy.
Bonus points if your pieces are covered in anti-tarnish fabric (usually a heavyweight double-napped flannel) or with anti-tarnish strips, and stored with silica gel packs to reduce humidity.
Why does silver tarnish?
Sterling silver is comprised of 92.5% silver and about 7.5% other metals, usually copper.
Oxygen causes silver to tarnish, so even just exposure to air will cause it. Contact with skin and haircare products, as well as perfume, accelerates the tarnishing process.
Humidity and air pollution also contribute to tarnishing in a huge way - in fact, silver reportedly didn’t tarnish at all before the industrial revolution.
There’s lots you can do to prevent your jewelry from tarnishing in the first place.
First off - wear it! Nothing keeps tarnish away better than contact with the body, because of friction from the skin. Tarnish has trouble building up when in constant contact with your body.
Remove your jewelry before swimming or showering. Try to keep it out of humid environments, so take it off in your bedroom before you go shower.
When you’re not wearing it, store your jewelry properly.
You probably noticed that most of these instructions are for removing tarnish from silver jewelry. That's because 14k solid gold contains fewer oxides, so it won't tarnish or discolor from contact with oxygen.
All your gold jewelry needs is an occasional light polish with a soft, chemically-treated polishing cloth. You can also gently scrub it with a soft-bristled toothbrush and warm water.