Add 1 gallon of warm water to a 5-gallon bucket. Mix a few drops of liquid dish soap into the water with a wooden spoon.
Dampen a cloth in the mixture. The cloth must be damp but not dripping wet.
Scrub the wood furniture with the cloth. This will remove the greasy film that cigarette smoke leaves behind. Wring the cloth out in the mixture when it becomes dingy.
Rinse the mixture off the wood furniture with a clean cloth dampened in cool water. Dry the wood furniture with a towel.
Dump the mixture from the bucket and rinse clean. Fill the bucket once again with 1-gallon of water. Pour 3 cups of white vinegar into the water.
Scrub the wood furniture with a clean sponge saturated in the vinegar-water mixture. Vinegar is an all-natural deodorizer and grease remover that will thoroughly clean the wood furniture while removing the cigarette smoke odor.
Allow the vinegar mixture to air dry on the wood furniture.