Place a folded piece of thick paper towel over the water damage on the wood. Avoid paper towel with ridges -- a flat towel is better.
Set the iron on the lowest heat setting. Pass the iron over the folded napkin and leave it for no more than two seconds. Lift up the towel to check the stain, and repeat until the stain is lightened.
Use a hairdryer instead of an iron if the water damage is on a part of the furniture that is curved or recesses and an iron won’t sit flat on it.