While the Corridor Trails are well-traveled and well-marked, you'll need to stop by the Visitor's Center (located on either rim) for "The Guide," which contains maps and tips, as well as updates about current conditions. Planning a route ahead of time, for a lot of people, is part of the thrill. Visit the National Parks Service site to sketch out the best route for your needs.
While the park is free and open, it's easy to get turned around and lose your way, so a map and compass are key. It can be easier than you may recognize, from the safety of your living room, to mistake one offshoot or minor trail for the main route, and keeping track of your location is an important part of the journey. Likewise, understanding the progression of milestones and distance markers in theory can help you recognize them in practice, and keep your descent on track instead of stranding you in the wilderness.
There is no cellular reception in the Grand Canyon, and while park rangers patrol the corridor trails regularly, emergency call stations are few and far between. By considering your route in terms of segments, moving from landmark to landmark, you can take in the beauty of your surroundings without getting lost in them. This is an especially important part of planning your descent, as the difficulty of the hike itself can distract you from remembering your direction or goals: Do the work ahead of time, as part of your preparedness, and you can take some of the hassle out of an already high-pressure adventure.
Along with maps, you'll also need a gallon of water per day per person; food -- eat something every time you stop for water to avoid medical complications -- with a good mix of protein, carbs and salt; protection from the sun for your eyes, face and skin; a knife and mirror, and just in case, a flashlight. For overnight stays, you'll want to bring a water filter or iodine tablets, toilet paper and a trowel, bags to pack out your trash, bathing supplies, and bug spray. It's not advised that you sleep under the stars -- snakes and scorpions, in particular, abound -- so you'll need some night protection as well. Use your hiking know-how! If you're making this very advanced trip, it's to be assumed you already know what else you're going to need.