Examine the table top carefully, looking for any dark spots or large stains. Apply a small amount of baking soda to those stains and then sprinkle distilled white vinegar on top. Rub the mixture into a paste and let it dry on the Formica. Wipe off the solution with a damp sponge and repeat if the stains remain.
Tear off a large piece of aluminum foil and turn it around so that the dull side faces up. Pour distilled white vinegar onto the aluminum foil and briskly rub it over the legs, backs and any other chrome surfaces on the chairs. Repeat the procedure on the table legs and the metal ring around the table. This removes scratches and other damage.
Pour a few teaspoons mild detergent and 1 gallon warm water into a plastic bucket. Dunk a sponge in the solution and use it to clean the vinyl on the chairs. Rinse the sponge out in cold water and use it to wipe away any suds or soapy residue from the vinyl.
Purchase an epoxy that closely matches the color of the Formica. Dip a wood craft stick in the epoxy and apply a thin coat to any surface scratches, chips, gouges or other damage on the table top. Dip a cotton ball in rubbing alcohol and lightly rub it across the epoxy, until it sits flush with the Formica. Let the epoxy dry overnight.
Clean the table top with traditional glass cleaner. Spray the glass cleaner on the table and wipe around the table with a paper towel. Use more paper towels to gently buff the Formica and remove any residue left behind by the glass cleaner.