South Rim Desert View (24 miles east of Grand Canyon Village) is open all year - Lodging is not available at Desert View. However there is a "first come, first serve" campground that is open from Sunday, April 16th through mid-October, 2017 (No hook-ups)
North Rim has a short season: Lodging is available May 15th through October 15, 2017.
Phantom Ranch at the bottom of Grand Canyon - is open all year.
Beginning in January 2019, reservations will be made through an online lottery system. More.
Camping Reservation should be made well in advance. Park campgrounds are full much of the year.