How can I remove water marks from a solid wood dining table?

Use white toothpaste (not gel) and a damp cloth. Rub lightly in a circular motion.

You can also try rubbing any type of oil in a circular motion with a soft cloth.

The easiest way is to get a handkerchief, lay it over the mark(s) and iron it. The iron should be reasonably hot but not maximum. keep the iron on the hankie for a few seconds at a time and keep repeating this until the watermark is gone. I once did the whole top of a timber coffee . The marks disappeared completely and never came back.

I agree with Jan. The iron idea is a good one. Just make sure the cloth you use is white. it only takes a couple of swipes of the iron. good luck