Polishing silver with... Toothpaste! Yes, I'm serious, that stuff that keeps your pearly whites white, will keep your sterling silver shining! So, let's say you have a blonde moment and go swimming at the pool with your silver ring on (I may or may not have done this). By the time you get done, it looks about like this:
So then, all you have to do is pull out a soft bristle tooth brush,and some regular paste toothpaste (don't use the gel toothpaste, it doesn't work as well), and scrub off all the icky black. With a little elbow grease, your jewelry will look good as new!