First thing is determine what the finish is, age may help w/that. Is this new ? ( if so, think about warranty from the store/ins. claim, I did many of these for a 3rd party warranty repair service) and then, go from there. Shellac will react w/alcohol, varnish will not. Catalyzed lacquer requires a major fix if it is that, reg. nitro cel laq. doesn't. Mohawk finishing supplies makes a kit for this for professional fixes, but again, it depends on what the finish is, and over the web, it is real hard to advise, esp. w/out a pic. and more info.
My mother and I have used Rotten Stone and Linseed oil. Takes a little elbow grease. I think you should be able to purchase the Rotten Stone and Linseed Oil at a hardware store-like True Value. If not, then look up on-line. We just use a rag to work it in, but follow directions.
Here's something I found on the internet: www.dummies.com/how-to/content/how-to-remove-water-stains-from-wood-furniture.html
You can try some "white ring remover" if that does not do the trick you may need to bring in some pro help as @Spheramid Enterprises mentioned above. I have done some spot work with lacquered pieces as well and poly and shellac. You need to know what you have to proceed.