I always recommend that you store your sterling silver jewelry in a plastic zip-top type of bag when you are not wearing it. The less exposure to oxygen, the less tarnish!
We all have those favorite pieces that need an extra bit of TLC! A friend showed me this article that explains the chemical reaction you can create with a simple non-toxic solution of baking soda and salt, hot water, a glass dish, and aluminum foil. I tried it on a number of different pieces and it didn't affect the aurora borealis coating on the crystal, which is always a concern when using commercially available silver dip products.
Here is the link: