Theodore Roosevelt National Park and a few other units of the National Park System are unusual in that they have several "islands" that are separated by other public or private lands. That adds a little challenge to negotiating this park, but nothing that a little advance planning can't solve.
The park is comprised of three separate units: the North, South, and Elkhorn units.
Park headquarters is based in the South Unit at Medora, North Dakota. It's right off Interstate 94. At Medora, you can check into the Visitor Center to get your Passport to Your National Parks stamped, pick up some reading materials and souvenirs, and then head out to drive the Scenic Loop that runs through the interior of the South Unit.
There are several nice pullouts and trailheads along the Scenic Loop to factor into your visit. Just up from the Scoria Point Overlook you'll come to the Ridgeline Trail, which is a great introduction to the park's badlands. There are several prairie dog towns along the drive -- one just north of Medora as you head to the scenic drive, one just as you turn right onto the scenic drive a short distance past the Cottonwood Campground, one near Boicourt Overlook, and one near the Beef Corral Pullout.
To reach the North Unit from Medora, you need to head east a bit on I-94 to Belfield, then go north on U.S. 85 for 54 miles. Turn left and you'll be at the Visitor Center, which like its companions at the South Unit and the Painted Canyon Visitor Center, also has some nice book selections as well as park souvenirs, postcards, water bottles, and a place to stamp your Passport.
There's one 14-mile-long Scenic Drive in the North Unit that leads you past some nice pullouts, the Juniper Campground and the Cannonball Concretions exhibit, some trailheads, the River Bend Overlook, and finally Oxbow Bend.
However, road sloughs have forced closure of this road beyond the Caprock Coulee Nature Trail. Park officials do, however, hope to have the necessary roadwork completed by fall 2012.
The Elkhorn Unit is the most difficult of the three to reach. From Medora, you need to get back on I-94 and head west to exit 10, then head north on County 11, a dirt/gravel road, to Forest Service Route 708. It's a scenic drive, but not one to rush.
Another approach to the Elkhorn Unit requires a high-clearance four-wheel-drive: When river conditions allow, you can ford the Little Missouri from a gravel access road found near the northern end of the South Unit's Scenic Loop Road. If you think this is for you, check with a ranger at a visitor center to see what the river conditions are.
You can see the two routes to Elkhorn Ranch on this park PDF.