Clean off the surface of the wood with a commercial wood cleaner and a soft, lint-free cloth. You must remove dirt, dust and other potentially abrasive materials before buffing the furniture. Otherwise, you risk creating further scratches.
Apply a small amount of wood furniture polish containing either orange oil or lemon oil to the furniture. Alternatively, mix equal amounts of lemon juice and olive oil in a small bowl. Whisk the two ingredients until they are well-incorporated.
Buff the polish or olive oil mixture into the wood with a microfiber polishing cloth. Blend the polish into the wood using small, circular motions. Keep buffing until the scratches disappear and the wood returns to its original luster.