You only need a reservation if you want to stay at a lodge or campground. There's plenty of parking at the park and free shuttle buses. The park entry fee is $35 per vehicle. Well worth it.
Everything mentioned above is accurate but also, if you plan on any hikes now in the winter, you'll definitely need microspikes (like crampons) to make it down the trails. The nearest rentals are in Flagstaff. Keep that in mind.
We were just there on Thursday. We bought the park admission from a gas station on Rt 40 & Rt 64 at a vending machine. Saved $5
You won't need reservations to just park, but you do need to book any lodging you're interested in. You also need a backcountry permit if you're planning to camp (i.e. in the Canyon itself). I recommend visiting the park's website.
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