If possible, remove water rings from wood furniture while they´re fresh by rubbing with a soft cloth. If water rings are set, you can apply an oil-based furniture polish. There are several other techniques you can try. You can apply mayonnaise liberally over the water ring and leave overnight, then wipe off with a soft dry cloth the next day. You can also try appling a small amount of non-gel toothpaste and baking soda to a damp cloth, then rub the stain lightly. Another technique is to apply a paste of cooking oil and salt, wait 15 minutes, then wipe off and polish as usual.
