We use Wright's Silver Cream for cleaning antique sterling silver. We found it to have very low abrasion comparing to other silver cleaning creams.
Add some to a dry microfiber cloth, rub it onto the silver, wash it off and dry with a clean microfiber cloth. We had the best results using microfiber clothes. They retain the cream well and will not damage the surface. Important: don't add the cream to a damp cloth! It will not work how it should.
For very light cleaning with almost no abrasion, when the surface is only lightly tarnished or delicate, use the sponge included into the jar.
By the way, this cream won Good Housekeeping recognition!
Enjoy your shiny silver!