What is the best way to clean tarnish from estate jewelry

Before answering, a word of caution.  Collectors of Estate Jewelry very often want the piece left "as-found" with tarnish and all.  Often the tarnish, or patina, lends an effect to a piece of jewelry that is desirable and represents, in part, the character of the item after years and years of wear and ownership.  So before committing to cleaning away the tarnish or patina, ask if that's really what you want to do.  Also, if purchasing an item from us with patina, and that you choose to remove, then the item is considered altered and, therefore, not returnable.
That said, where we find a tarnished piece of jewelry and it is clear to us that removing the tarnish will enhance, not detract from, the beauty of the item, we use a jewelry cleaning cloth.  These cloths are embedded with a cleaning solution that gently removes the tarnish with no or minimal abrasion.  Our choice are the Sunshine Jewelry Polishing Cloths for Sterling, Gold, Brass, Copper, and etc.  These can be inexpensively purchased at Amazon.com.