Exploring Petrified Forest National Park by car is easy; there's only one road that cuts through the middle of the park.
You can enter the park in two places:
Get off Interstate 40 at Exit 311 and enter at the Painted Desert Visitor Center, or take Exit 285 at Holbrook and then U.S. 180 19 miles south to the Rainbow Forest entrance.
Once inside the park, either at the north end or the south end, you have one option: the 28-mile road that runs between the two visitor centers.
There is one short spur to the east, about halfway between the two visitor centers, that leads to Blue Mesa. If you find your vehicle in need of fuel, there's a gas station next to the Painted Desert Visitor Center.
Something else to keep in mind: The park closes at night. The times differ throughout the year, depending on the season, but generally the park is open from 7 a.m. to 8 p.m. during the height of the summer season. You can find the exact hours throughout the year at this page.