Use paper towels to blot up any standing water. Spray on some furniture polish and rub it in with the paper towels. Sometimes this is enough to clear up surface rings.
Squeeze a thin line of toothpaste onto the water ring and rub it in with your fingers. Wash your hands immediately so you don't accidentally touch your eyes, and then buff the toothpaste in with a clean cloth. Wipe it away with clean, dry paper towels. This can abrade a surface stain down enough that it can't be seen. This method is best for marble tables.
Spread two to four tablespoons of mayonnaise on the water ring and rub it in with a soft, lint-free cloth. Let the mayonnaise sit overnight, and then wipe it all off with clean, dry paper towels. The oil in the mayonnaise will often restore the discolored wood. This also works very well on leather tables.
Place a sheet of waxed paper on the water ring, and lay a soft, clean cloth on top. Using the iron on its lowest setting, press the cloth in small circles. Set the cloth aside, carefully peel up the waxed paper, and the stain should be gone.
Use 220-grit or finer sandpaper to gently buff the finish and stain off of the water ring. Wipe up any dust, and then re-stain that spot with a matching stain applied with a staining sponge. Feather the edges do that you don't have a line between the new and old stain.
Eliminate very old and stubborn water rings on wood tables by sanding and re-staining the entire table top. Let the stain dry and seal it with two to three coats of polyurethane to prevent future stains.