Wipe the area with a dry cloth to remove surface moisture and move a hair dryer slowly back and forth over the wet area. Allow to sit overnight and then apply lemon oil or other high-quality polish to the wood if no evidence of a stain appears.
Apply regular white toothpaste to the stain with a cloth, rubbing with the grain of the wood. Allow to set overnight and remove with a soft, damp cloth. If any of the stain is still evident, repeat. After you remove the stain, apply lemon oil and polish to a sheen with a cloth.
Mix cigarette ashes into a thick paste with lemon juice and rub into the stain. Allow the paste to dry overnight before removing with a soft, damp cloth. Repeat the process if needed, then polish the surface of the wood with lemon oil and a cloth.
Combine baking soda and water into a thick paste, rub into the stain thoroughly with a cloth, and allow the paste to dry at least 12 hours. Remove with a dry, soft cloth, rubbing diligently with the grain of the wood. This method does not work quite as well as the cigarette ashes and generally requires repeating the process. Wax or polish the table after the stain is removed.
Coat the water ring with mayonnaise or salad oil, rubbing well into the surface with the grain of the wood. Wipe off the surface and polish with a dry, soft cloth.