Unfortunately, there are no front-country campgrounds at Petrified Forest National Park, so if you want to pitch a tent, you'll either have to head off into the wilderness backcountry, or look for the nearest private campground.
If you're a backpacker, there's space to roam, but you'll need a strong back as there are no water resources to quench your thirst. Instead you'll need to pack in all the water you'll expect to need. And in summer that can be quite a lot under a hot sun with little shade to be had. Park officials recommend a gallon a day per person.
And while there is a lot of wood in the backcountry, you'll find little to burn, as far and away most of it has been turned to stone. And if you do come across burnable wood, well, park regs prohibit you from burning it.
Most backpackers tend to head into the Painted Desert Wilderness that lies north of the Painted Desert Inn. You can find parking and a trailhead at the inn. Once you head down the trail, you need to walk at least a mile, past Lithodendron Wash, before setting up camp.
You also can backpack into the wilderness area in the south end of the park.
Whether you go north or south, you'll need to pick up a free permit at either the Rainbow Forest Visitor Center, Painted Desert Inn, or Painted Desert Visitor Center at least one hour before the park closes for the night.
And remember, no collecting of fossils or petrified wood, and keep a sharp eye for petroglyphs. Take plenty of pictures, but leave them behind for the next desert wanderers to enjoy.
If you want to pitch a tent, but not have to carry it into the backcountry first, there's a KOA facility in Holbrook, some 21 miles west of the park off Interstate 40.
Traveler trivia: Petrified Forest, and Craters of the Moon National Monument and Preserve in Idaho, were the first units of the National Park System to have wilderness areas officially designated within their borders, in October 1970.