These form when moisture from a drippy glass or a hot dish gets trapped in the finish. To remove a long-standing stain, place a towel on top and press with a warm, dry iron for five to 10 seconds — this will soften the finish enough to release the moisture. Candle wax and crayon respond well to ice. Fill a plastic bag with ice cubes, wrap it in a towel, and place it on the stain until it hardens (a few minutes); carefully coax wax off with a plastic spatula or a credit card.
Hide them with touch-up markers like those from Parker & Bailey ($6, ParkerBailey.com), which we tested and found effective. Dab (don't color) a scratch with the lightest marker in the kit, then use a darker one if needed. Wipe off the excess with a soft cloth before it dries, and finish with a polish.