You'll need a permit for all overnight use of the backcountry -- which is to say, anywhere besides the dorms and cabins at Phantom Ranch -- which is one of the first hurdles you'll be clearing as you plan your trip. They can be tough to get, requiring you to apply three months in advance (there's a last-minute walk-in waiting list for backcountry permits, but the parks service warns that could take up to three days of applying in person, so don't chance it) -- this trip is one you should really plan at least a year beforehand.
Because of the necessity for protecting the rich canyon environment, these permits come with a host of caveats and rules. You can't deviate from the itinerary you've been allowed, because the permits themselves are granted with an eye toward balancing use of various areas within the park. Behind the scenes, park administrators make these decisions based on group size, timing and available resources. There's a lot of work that goes into providing hikers with access to this gorgeous natural wonder, and not all of it is immediately apparent.
Unlicensed use of the park, off-itinerary overnights, or trying to cheat the system by splitting into smaller groups and reconvening later all come with fines, penalties, court appearances and possibly being escorted from the park by rangers, so understand the rules and make sure you follow them. After all that effort and preparation, the last thing you want to do is have the trip ruined over a simple mistake or careless oversight.