Create a cleaning paste in a quantity large enough to cover your copper-topped table. Combine 1 cup vinegar with 1 tbsp. salt. If you want a larger amount of paste, use 2 cups vinegar and 2 tbsp. salt. In each case, mix the vinegar and salt with enough flour to form a thick paste.
Apply the cleaning paste to the copper-topped table. Spread it across the surface, making sure areas of heavy staining are well-covered. Leave the paste on the table for at least 15 minutes, but it's safe to let it remain for as long as an hour.
Remove the paste using damp cleaning rags. Rinse them often in a bucket of warm water, and wring them out well.
Scrub any areas of staining which fail to come off with a green scrubbing pad or an old toothbrush. Once the paste has been completely removed, dry and buff the copper-topped table using microfiber cloths.