self-service launderettes are available on some (but not all) of NCL's ships. Please note that using irons in cabins is prohibited, as they are considered a major fire hazard. For in-cabin use, a portable steamer is a much better and safer alternative.
To add upon what Raoul wrote, the NCL ships with self service laundries are the Dawn, Jewel, Jade (ex-Pride of Hawaii), Pearl, and Gem.
There are a few washers, dryers, and irons with boards in each self service laundry, all free for use. There's also detergent available from a vending machine for a small fee ($1 if I recall correctly).
I have read on other web sites that sometimes your room steward will bring an iron and board upon request to your cabin. But in these instances, they can't leave the general area until the iron and board are returned.
I wouldn't use an iron anywhere without a board.
You wouldn't use an iron on your wood furniture, nor on you own bedding at home, why do so many believe it's perfectly okay to do so on a cruise ship?