Pour 1 quart of warm water into a small bucket. Add 3 tablespoons of baking soda. Stir the solution with a mixing spoon and allow the baking soda to dissolve into the water completely.
Submerge a clean, soft cloth into the bucket of cleaning solution. Allow the cloth to become saturated, then wring it out the excess water.
Wipe the entire surface of the marble table top. Scrub harder on areas of tough grime. After you have wiped away all stains and grime, leave a thin layer of the cleansing solution covering the table top.
Allow the cleansing solution to dry on the marble table top. Let it sit for 2 to 3 hours.
Wet a clean soft cloth under a stream of cold water. Wring it out and use it to wipe the cleanser of the marble table top.
Dry the marble table top with a clean soft cloth.