The shortest route, via the South Kaibab and North Kaibab Trails, is 41.8 miles. The longer, less popular route, via the Bright Angel and North Kaibab Trails, is 46.6 miles. It is possible to take the South Kaibab down and the Bright Angel up, or vice-versa, in which case the distance would be 44.2 miles. (Note: The South Kaibab and Bright Angel Trailheads are about 3 miles apart, both reachable via car, shuttle, and foot). Download the Water Chart & Databook to see a breakdown of these distances.
The South Kaibab Trailhead (at the South Rim) is at 7,260 feet, the Colorado River is at 2,400 feet, and the North Kaibab Trailhead (at the North Rim) is at 8,250 feet. Total elevation gain is 10,710 feet , and ditto for elevation loss. Total elevation change, up and down, is 21,420 feet. In short, a lot.