Fill a bowl with undiluted white vinegar.
Place the metal drain ring in the bowl with the vinegar, and allow it to sit for at least 30 minutes.
Rinse the vinegar off the ring thoroughly so there is no danger of the acetic acid damaging the rest of the metal.
Scrub the rust off using a nylon scrub pad or a piece of fine-grit sandpaper if you were unable to get all the rust off with vinegar. A mild cleanser such as baking soda or sodium borate is often successful in restoring the luster of metal.