Put on a pair of rubber gloves to protect your hands from the nicotine residue, as well as from the cleaning products.
Pour mineral spirits over a soft white cloth until it is soaked. Wring it out lightly, and then use the damp cloth to wipe down the wood furniture. According to Utah State University, mineral spirits can remove oil and grease, yet are safe to use on wood. You may need to re-wet the cloth if the nicotine covers a large area.
Wash the wood furniture with an oil soap designated for use on wood. Follow all directions on the packaging label, as most oil soaps must be diluted before they can be used to wash furniture. This will get rid of the mineral spirits and further help remove the smoke odor.
Polish the wood furniture with lemon oil and a lint-free cloth. The oil will restore shine to the wood furniture, while the lemon fragrance replaces the smoke smell with a pleasant citrus scent.