A natural property of sterling silver is that it will tarnish when exposed to air, more with some peoples body chemistry than others. When you are not wearing your jewelry, keep it sealed in a plastic bag so that it is not exposed to air. To keep the piece shiny, use a jewelry cloth to polish it. To maintain a satin finish, use mild soap, water, and a scotch brite pad. Avoid rubbing the scotch brite pad over any stones or polished areas. A soft tooth brush with toothpaste or Mr. Clean can also be used to loosen any dirt and oil on the piece.
A liquid dip cleaner can remove the oxidation that occurs around details of the piece, like the stone settings or patterns. These details are enjoyed by some people, because it personalizes each piece. If you don't want the dark details removed, do not use a liquid cleaner, just a toothbrush and Mr. Clean, then dry and use a polishing cloth. Most cleaners and cloths can be bought in the jewelry department of major department stores.