Remove the existing table top finish and stain in color desired. You can do this yourself or send it to a furniture refinisher.

You don’t think it would look weird to have a different stain on top than on bottom?

Scrape the table to bare wood and refinish. Don't use sandpaper, and use aniline water based stains for the refinish with shellac secondary coats, finish with a poly topcoat. If you don't know how to do this, best to have it done professionally.

I think it would look very odd to have the top and the bottom finished in a different stain.
You can try a "quick and dirty" fix and if that doesn't fix it to your satisfaction, then do a full refinish. Try mixing 2/3 shellac thinner with 1/3 lacquer thinner and, in a small area at a time, brush it on....let it sit for about a minute and wipe with a paper towel. Do in a well ventilated place, and be careful not to drip the solution on other parts of the table...if it does drip let it dry in place and do not try to wipe it.
When it is all even looking, then finish with 2 coats of polyurethane varnish.

If you choose same color stain as the original table color, the top and bottom would be same color.