What is the best way to remove or cover white places on an oak table?

white places????water marks or heat stains???Is there a finish on the table?

It sounds like heat spots. Here's an article that should help:

https://www.bobvila.com/articles/how-to-remove-water-stains-from-wood/#.Wg-PqExFw7I

Best of luck with your cleaning project!

i'm not being a wiseguy, but why don't you just put a pretty tablecloth on your table?

Sand the table top and restain it. Easy answer if the one above put a tablecloth on it.

Best of luck. I hope you can find a solution that works.

Before you start sanding and try to refinish the table try a product sold and auto stores. Its made to remove swirl marks made when waxing a car. It works on either heat or water marks. It comes as a cream or paste. Put it on the marks and let it sit for about 30 min. Use a clean dry cloth to wipe off and buff the area. If some of the marks remain repeat until the marks are gone. I have never had it not work at least not on any I have done. Its always worth a try before going to all the work of refinshing the table.