How to care for the finished surfaces of furniture and other wooden objects is a lesson of "ifs". If the finish is wax... If the finish is shellac... If the finish is varnish... It goes on! However there are some universal caveats that apply. Avoid using both liquid and spray polishes and polishes or waxes that have silicone in them. First, liquid polishes allow the polish, through capillary action, to migrate through any cracks in the film and those cracks in the wood that will contaminate the wood and/or the glue line. Oils especially can work their way deeply into the wood, forever staining it. Polishes and waxes that contain silicone make future restoration of the finish problematic (I'm being kind). Silicone is not removed easily and should it make its way into the wood, may be permanent. So what's the problem? It will interfere with the adhesion of both glues and finishes to the wood.
There are recipes out there that promote oil, mayonnaise, cigar ash, lemon oil, alcohol, linseed oil, and various concoctions. These things separately and in combination can cause chemical changes to the finish that cannot be undone, sometimes actually removing some or all of the finish.
What is the homeowner to do? Without knowing the composition of the finish–shellac, lacquer, wax, varnish–the safest thing to do is clean the surface with a just-damp cotton cloth. Next on the safest things, but not completely safe, is to use a solid wax and follow the directions on the can. However, if the finish is a modern finish that has a low sheen (dull) by design, wax will change that sheen to something you weren't expecting. On the solid wax treatment, crayons can touch up a wide variety of scratches and blemishes. (Binney Smith's Crayolas® are perfect. Having swapped out the colors I need and replaced them with colors I didn't need, my children knew nothing of black and brown crayons!)
Without knowing what the composition of the finish is, other treatments are simply guesses and could be disastrous. Solid, non-silicone waxes will serve for most situations where someone wants to improve a "dry" looking surface. And even then, a once-a-year treatment is adequate.