Camping is very limited and is on a first come first serve basis. Occupancy is also based on bird migration. The more migration the more people visiting. Since there is a 3 day stay limit, turnover is quick. The camping area is nothing but what looks like a parking area so look for the "Overnight Camping Permitted" sign. Don't be surprised if many spots are taken by day visitors who clear out after dusk.
I would suggest if you have never been to WWD, call the Arizona Dept of Fish and Game's office and they can give you some advice as to busy period and such.