Combine 1 tablespoon of water and 1 tablespoon of baking soda in a bowl to create a paste. Rub the paste onto the white ring with a washcloth in a gentle circular motion to remove the ring. Wipe the paste off the furniture with a damp washcloth.
Pour 2 tablespoons of vinegar and 2 tablespoons of olive oil into a bowl. Stir the ingredients and then dampen a washcloth with the solution. Wipe the solution over the white ring in the direction of the grain, then wipe the furniture with a dry washcloth.
Mix 1 teaspoon of table salt with 3 to 4 drops of warm water to create a paste. Rub the salt paste over the ring with a nonabrasive sponge to remove it. Wipe the remaining paste off with a damp washcloth.
Lay a towel over the water ring. Set an iron to a dry "Low" setting and rub it over the towel carefully; do not touch the wood surface. Allow the towel to soak up the moisture that the heat releases from the wood. Remove the towel from the furniture to look for the white ring, and repeat the process until you remove as much of the moisture as possible.
Run a hair dryer on its lowest setting over the white ring. Move the hair dryer over the stain slowly until it causes the moisture to evaporate completely.
Apply lemon oil to stubborn white-ring stains. Rub the lemon oil onto the stain with a fine-grade steel wool to remove the white ring. Press down with a slight pressure; if you press down too hard, you may leave behind deep scratches.