Wrights or Goddards silver polish.
Before you clean any sterling silver make sure that what you have will not lose it's value if you clean it.
I use an old-fashioned method my grandma taught me, she used it for years and it works without damaging the sterling silver. Use Pepsodent or plain old regular Colgate toothpaste. With a soft cloth, gently rub the toothpaste in circles onto your silver piece until the tarnish is gone. Rinse thoroughly with cold water. Work in small areas of the piece. I've never applied it over an entire piece and waited to rinse.
Janna: try Tarnex
Here is a video to help
I sell a lot of silver on Ebay. Jewelry, silverware, serving sets. Silver polish like Wrights and dips like TarnX tend to remove some of the metal. The foil method doesn't work that great and still leaves a grey film that still needs to be removed. I use white toothpaste (not gel) and a damp toothbrush. For large items I use a damp cloth. Also works on copper, brass, gold, porcelain, ceramics, sneakers, plastics, etc. For my sales I needed one product for cleaning everything.
Lots of ideas here: