Depending on how bad the tarnish is, Limelite (limescale remover) works. The only thing it doesn't do is prevent the tarnish coming back. The best thing to use is Brasso, it smells awful but does the job and keeps it tarnish free for longer. One thing you can do after the brass has been cleaned is to coat the item using metal lacquer (get it from craft shop or similar) - it dries quickly and prevents tarnishing (which is caused by oxidisation - eg, exposure to air). Brass items such as door handles do not tarnish because they have been lacquered).