How dirty is it, and what is the dirt? I'd start by hand buffing with a soft cloth; that should get any loose dirt off and could even work on light tarnishing.
Heavier tarnish is easily cleaned off with commercially available silver polish (look in the cleaning section of your grocery store).
Tarnish can also be removed electrolytically, but I'd only recommend this if the sterling parts can be removed from the non-sterling parts. Mix equal parts baking soda, salt, and liquid soap, dilute with a lot of water, and put it in an aluminum pot (or a pot lined with aluminum foil). Put the sterling in the pot, bring it to a boil, and let it stand for a few minutes. Then rinse and wash the sterling. (Oxides get transferred to the aluminum.)