The best way to see Grand Teton National Park is by car. Unlike Yellowstone's Grand Loop, Grand Teton's road system doesn't allow for easy tour-bus access to all the major sights. Only a car will get you close to Jenny Lake, into the remote east Jackson Hole hills, and to the top of Signal Mountain. You can stop at many points along the roads within the park for a hike or a view. Be extremely cautious in winter, when whiteouts and ice are not uncommon. There are adequate road signs throughout the park, but a good road map is handy to have in the vehicle.
Jackson Hole Highway (U.S. Highway 26/191/89) runs the entire length of the park, from Jackson to Yellowstone National Park's south entrance. (This highway is also called Route 26/191 south of Moran Junction and U.S. 287/26 north of Moran Junction.) This road is open all year from Jackson to Moran Junction and north to Flagg Ranch, 2 mi south of Yellowstone. Depending on traffic, the southern (Moose) entrance to Grand Teton is about 20 minutes from downtown Jackson via Highway 89/189 (Broadway Avenue), then right onto Wyoming 22 west and right at Wyoming 390 north (aka Moose-Wilson Road). Coming from the opposite direction on the same road, the northern boundary of the park is about 15 minutes south of Yellowstone National Park. Also open year-round, U.S. 26/287 runs east from Dubois over Togwotee Pass to the Moran entrance station, a drive of roughly an hour.
Grand Teton Lodge Company has shuttle service to its lodging properties, but if you drive, which is recommended, there is plenty of free parking at all developed areas and adequate parking at waysides and historic sites. Although break-ins aren't common, use good sense when leaving your vehicle for an extended period of time by locking valuables out of sight or taking them with you.
Two back-road entrances to Grand Teton require high-clearance or good-performing vehicles. Both are closed by snow from November through May and are heavily rutted through June. The Moose-Wilson Road (or Route 390) starts at its intersection with Route 22 in Wilson (4 mi west of Broadway Avenue in Jackson) and travels 7 mi north past Teton Village, then turns into an unpaved road for almost 1 mi until the Moose entrance. It's closed to large trucks, trailers, and RVs. Even rougher is 60-mi Grassy Lake Road, which heads east from Route 32 in Ashton, Idaho, through Targhee National Forest. It connects with U.S. 89/287 in the John D. Rockefeller Jr. Memorial Parkway sandwiched between Grand Teton and Yellowstone.