Water rings that are on furniture with an oil or lacquer finish can usually be fixed pretty easily. You will need a gentle abrasive. A good one to use is one you make yourself. Mix one tablespoon baking soda with one teaspoon water. Put the abrasive on a damp cloth and gently rub the spot in a circular motion with the abrasive until it disappears. Then dry the area with a soft cloth and seal the finish with furniture or paste wax.
If you don’t have any baking soda, you can use a nonsoapy amonia or a nongel toothpaste.
Another method is to mix equal parts of vinegar and olive oil. Apply it with a soft cloth and rub it on the furniture as above. Use a clean, soft cloth to shine it up.