I haven't done laundry at AKL, but the washers are $2.00 per load and the dryers are $2.00 for 30 minutes of drying time. If the dryers are anything like the ones I've used at other resorts (YC, CSR and PC), they tend to run hot, so check the temperature setting if you have anything remotely delicate.
Edited to add:
Be sure to take your room key card with you. You may need it for access to the laundry facilities. It doesn't seem to be consistent when you need it, regardless of what is posted.