That is already stained and finished. Those water marks are caused by water reacting with the finish. Probably lacquer.

If you want to try and add stain, you first have to remove all---and I do mean all of the finish. That is very difficult without dipping the table(the way professional stripping companies do).

However, if the finish is lacquer, that means fixing the water marks is fairly simple. Test the finish with a rag wetted with lacquer thinner. If the finish dissolves a bit, it is lacquer. Sand the water spots away(don't sand deeply into the wood) and apply new lacquer. Lacquer is a finish that partially dissolves the previous coat no matter how old that previous coat. So, it is easy to spot finish, sand(with 0000 steel wool or the plastic equivalent) and get a smooth finish trepair.

Before I did anything drastic, I'd attempt to remove the water blush with a special cloth (see p. 5, as I cannot direct you right to that page). You can buy these directly, or better, at a local Bed, Bath, & Beyond, or many Lowe's, Ace Hardware, or Do-It-Best Hardware. It will leave behind a slightly oily film and make the table a bit glossy. You can remove the oil with a furniture polish.

If you really want to darken it a bit after you have removed the spots, the long route is strip and refinish. A lot of work. A short cut would be to spray on a lacquer toner. This will be a bit more difficult to find as you'll have to find a paint store that caters to professional furniture techs, or order from Mohawk or Guardsman. Should run about $6 a can. Remove or mask off what you don't want to color, and spray several light coats. Practice on a piece of cardboard until you get the hang of it. The worst mistake you can make is to get it on too heavy. It can run and look terrible or turn opaque in a flash. Better to put on 5 light coats and sneak up on the color than one heavy coat and miss.

Disclosure: I have a business relationship with Guardsman, and I use both Guardsman and Mohawk products, but have no financial interest in your buying either.

Here is a link that might be useful: Furniture care products.