When possible, it's best to try to prevent tarnishing. I have in the past, and had good luck so far with anti-tarnish strips. I purchased mine through Rio Grande, but I'm sure other suppliers probably have them available.
I have cleaned up lightly tarnished SS chain maille pieces in a tumbler with lead shot, a little bit of water and dishwashing liquid. Rinse, wipe with a soft cloth and then let air dry.
I came across this article and it sounds like a good tip for if you ahve something much more badly tarnished:
http://www.sterling-silver-jewelry-site.com/cleaning.htm
I hope this helps!
Sarah
Anyone have any suggestions on keeping my silver jewelry from tarnishing? Since I work with lots of sterling silver, my materials sometime loose their shine. I sometimes use a chemical cleaning solution but don't necessarily want to immerse finished works.