Pewter can be cleaned or renewed in several different ways. Wiping with a damp cloth can remove many stains or dust build-ups. If the item has a highly polished finish, some light tarnish can be removed with pewter polish (similar to polishing silver).
Do not use silver polish on pewter. You can obtain pewter polish at higher-end retailers who sell pewter serving items.
If the item has a satin or matte finish, you can rub it gently with very fine "0000" steel wool. It is best to try a small a spot on the bottom first to see how it looks.