Place 1/2 cup of hot water in a bowl. Add 3 drops of ammonia.
Dip cheesecloth in the ammonia solution and wring out excess moisture. Rub the diluted ammonia solution into the water stain on your mahogany table. Continue this for one to two minutes so the ammonia has time to draw out the moisture. Dry the surface with a clean cloth.
Lay a clean cotton cloth over the remaining stains caused by glasses. Heat a clothing iron to the lowest heat setting without steam.
Press the iron into the cotton cloth without moving it around. Hold the iron in place for three to four seconds at a time to draw the moisture out of the wood with the heat. Repeat this process for one minute to remove as much of the white ring as possible.
Apply a pea-sized amount of white toothpaste to a clean cloth. Buff the mahogany wood with the toothpaste to draw out any last traces of white water stain. Wipe the toothpaste off with a damp cloth and dry the table with another cloth.
Restore moisture to the mahogany wood table by buffing it with a nickel-sized amount of wood polish.