Clean the furniture with a soft rag and any commercial cleaning product listed for use on the material. Or you can use dish-washing liquid and water. Then wipe it dry with a clean rag.
Touch the surface in a few hours. If the tackiness is gone, then surface dirt or grime was causing the problem. Regular cleaning will prevent it from recurring. If the tackiness or stickiness remains, the problem is degraded finish. You must now clear away the finish to remove the tacky layer.
Moisten a rag with an appropriate solvent. Naptha or mineral spirits are ideal for removing sticky wax finishes. Lacquer finishes must be removed with lacquer thinner or denatured alcohol. How do you tell which finish is on your furniture? Most modern wood furniture is finished with wax. Lacquer, a hard, shiny finish, is not commonly used anymore but may be found on antique pieces.
Rub the surface of the furniture piece (always in the direction of wood grain) to remove the stain. As you dirty one section of the rag, move to a clean section. Re-moisten the rag if necessary. Removing the finish will take a lot of patience and elbow grease. As you rub, the finish will slowly break down.
Wipe the furniture clean with a dry rag.
Allow the surface to dry for 24 hours before applying another coat of finish.