Both camping and staying in the Lodge require reservations. There are differing nightly fees for camping and the lodge. These fee’s are charged per night. In addition there is a one time access fee, and a one time environmental fee.
A 10% tax may or may not be included in fee’s you see posted. They do charge tax.
Be sure to secure your reservations through an official Havasupai Tribal source to avoid being scammed.
In the past there have also been some Commercial Guide companies that you could reserve through and pay through. In some years this has not been an available option. These outfitters often provide many amenities and services at various additional costs. But it is always wise to find out through an official Tribal source which outside companies/outfitters may or may not be authorized during the time frame you wish to visit.