Varnished wood should be protected with a furniture wax. As wax and varnish are perishable, protect surfaces from water, alcohol, other liquids, foods and cosmetics. Table pads, glass tabletops and other coverings work best.
Dust regularly with a soft dry cloth. If finish is waxed, do not use oiled or treated cloths, as they may make wax sticky. Occasional rubbing of surface with clean, dry, soft cloth removes smudges and dust and leaves a sheen. Some varnish finishes may be wiped with a moist (not wet) cloth to remove fingerprints and light soil, followed at once by rubbing with a clean dry cloth. Test first on inconspicuous spot to be sure this does not damage varnish. Do not get varnish wet, or allow damp cloth to stand on it.
When dirt or grime have built up, clean with a solvent-based furniture cleaner polish, or wax. Use one that gives desired gloss compatible with varnish gloss, high or low luster. Most polishes and waxes leave a layer of wax on surfaces to protect finish. In cleaning, do only a small area at a time and wipe dry with clean cloth. Waxed surface may be buffed occasionally to restore shine. Re-wax if buffing does not restore a shine.
Excess wax or polish is an enemy. Remove it with a cloth dampened with mineral spirits or synthetic turpentine. (Natural turpentine may leave a sticky residue.) Should the furniture be badly soiled due to neglect, use very fine 3/O or 4/O steel wool instead of a cloth and rub with the grain of the wood. Some finishes can be damaged by prolonged contact with mineral spirits. Clean small areas at a time. Wipe each area with a clean cloth before going on to the next. Discard steel wool as it becomes soiled.
When using mineral spirits, turpentine, or other solvents, including solvent-based cleaners, follow all label warnings. They are flammable, so don't use near any flame, spark, pilot light, and don't smoke. Wear rubber gloves to protect your hands, and dispose of them afterward, or wash in hot suds and air dry. Air-dry cloths used in cleaning to evaporate the solvent before disposing.
Some varnishes may be washed if badly soiled. Test method first in inconspicuous spot; if it streaks, or turns white and hazy, STOP! If OK to proceed, use solution of mild detergent (hand safe dishwashing liquid) and lukewarm water. Use clean sponge or soft cloth. Wash, rinse and dry only a small area at a time, working fast to avoid over-wetting finish. Avoid excess water, especially around joints. When completely dry, polish or wax. In most cases, it saves time and energy to clean with furniture polish/wax in the first place.
Oil soaps may clean satisfactorily on some varnish finishes; test first in inconspicuous spot.