Water stains can completely ruin the look of wood veneer. This material can be very expensive, and it is also expensive to have a professional come and fix it for you. Instead of hiding the problem, try fixing it with materials you probably already have around the house.
Combine 1 tbsp toothpaste with 1 tbsp baking soda to form a thick, gritty paste.
Put the paste onto a clean cloth. Apply the mixture to the moisture stains on the veneer.
Work the cloth in a circular motion over the stain for 10 minutes to buff it out. Wipe the excess paste away with a clean paper towel.
Apply a wood polish directly to the affected area. Buff the polish in with another clean cloth. The stain will be gone.