What kind of damage is it?

If it is a white blush, you can treat it like a water ring (see link).

If the finish is flaking off, but the color is good, you can lightly sand to remove the flaked off finish. Then apply some aerosol lacquer in a sheen to match. This assumes that the original finish was lacquer, that is the 99%+ finish of choice on factory-finished furniture.

If the stain is black, it could be mold, or more likely a chemical reaction between the oak's tannins, water and any stray iron. The cure for this is to strip, reverse the chemical reaction with oxalic acid bleach (follow directions), then refinish.

Here is a link that might be useful: removing water blush