Green River is on Interstate 70 about midway between Denver and Las Vegas, 180 miles southeast of Salt Lake City and 50 miles northwest of Moab. Most people arrive by car — there is no bus service.
Amtrak's California Zephyr stops at the small Green River station once a day in each direction, between Salt Lake City and Grand Junction. The eastbound train rolls through in the small hours of the morning, the westbound in the early evening. It is not a quick way to get here but the canyon scenery between Helper and Green River is one of the great rail journeys in the American West.
The nearest large airports are Grand Junction (105 miles east) and Salt Lake City (180 miles northwest). Canyonlands Field in Moab handles a few short flights from Denver.