Blot--do not rub--the fingernail polish remover with paper towels. Continue blotting until no more of the nail polish remover can be absorbed.
Sand the area with a piece of fine sandpaper. Sand with the grain of the wood until you have removed the damaged or discolored wood.
Wipe the area clean with a damp cloth. Dry with a lint-free towel.
Use a paint brush to apply a wood stain that matches the undamaged wood. Brush the stain onto the wood with the grain. Allow the stain to sit for five to 15 minutes. Wipe the excess stain off the wood using paper towels. Once again, wipe with the grain. Repeat the process until the damaged area matches the rest of the wood.
Allow the stain to dry completely. Apply wood varnish and allow the wood furniture to dry completely. Wax and buff the furniture as you normally would.