Grind egg shells with pestal/Morter and mix them with real mayonnaise to make a paste.
Using your finger work it into the burn mark.
Let sit for 10 min. Work in some more and wipe off.
Basically the same idea but use cigar or cigarette ashes with mayo. Dip a damp cloth in the mixture and work into the stain. May take several applications.
I have also heard of using 1/2 and 1/2 toothpaste and baking soda but have not tried it.
Preventing water marks:
Put a good coat of butchers wax on the table using very fine steel wool and let it sit and dry. Buff off with soft cloths. Several applications build up a protective layer. I can put a sweating beer on my coffee table and leave it for hours with no damage.