It isn't difficult to remove watermarks from your wood tabletop if you act quickly and cautiously. Most things you will need you most likely already have around the house.
Step 1 - Quick Clean Up
As soon as you have a spill clean it up. Speed is the best weapon against a watermark that may be difficult to remove. Blot it gently, do not rub as you can rub the water into the surface of the wood instead of removing it. If you can, grab a blow dryer and move it around to let warm air blow gently over the wet surface. You may see the mark disappear before your eyes as the wood dries out. Watermarks are usually wet varnish and not actually wet wood.
Step 2 - Repair
If you still see a bit of a white mark or if you didn't find the spill in time to clean it up before it left a mark you may need to do a bit of a repair if the mark isn't too bad. Use an oil base furniture polish and gently work it onto the surface. Do the entire table to even it out. There are furniture oils made, such as Old English, that have a bit of stain in them to match your wood. This will take care of most marks. If the mark reappears, simply use the oil again.
If you don't have any oil, try an old fashioned remedy: mayonnaise. Dip your cloth into a bit of mayonnaise and work it onto the surface of the table just like you would the oil. Leave it on the surface overnight. The vegetable oil in the mayonnaise will refresh the wood and make the watermark vanish. Buff gently with a clean dry cloth the next morning.
Another old trick is to use cigarette or cigar ashes if you have a smoker in the house. Just rub the ash into the mark and watch it disappear. Do this gently for best results. Yet another trick is to use white toothpaste, not the gel type, and put a glob on the watermark and work it around a bit in a polishing fashion. This will usually buff out the watermark. You can also mix together a paste of baking soda and water and apply it to the mark. Leave it on until the next day then polish it off with a clean, dry cloth.
Any of these can be followed with the gentle heat cycle of a blow dryer to completely dry out the wood.
Step 3 - Refinish the Piece
In extreme cases or if the wood has many marks on it, the best thing to do is clean the wood with a good wood cleaner and 0000 steel wool. After that apply a coating of Tung oil or any finishing oil to restore the original finish of the table. You may also have to totally refinish the piece if it's very badly marked or damaged.