Distance: 2.2 miles (3.5 km) round trip for the lower grove; 5 - 6 miles (8 - 10 km) round trip for both the lower and upper groves
Elevation at trailhead: 5,600 feet (1,700 meters; 28 Grizzly Giants)
Elevation Gain: up to 1,200 feet (360 meters), depending on which parts of the upper grove you reach
Wait, don't look at this map: The Mariposa Grove brochure, available at the trailhead for fifty cents or as a free PDF download from the NPS website, includes a map that labels the most famous trees, a tricky thing to do with Google Maps, and shows supplemental trails that aren't included on this map. You should look at it before reading any further here.
Map Notes: The red line marks the trail through the lower grove, whose famous trees include the Fallen Monarch, the Bachelor and Three Graces, the Grizzly Giant, and the California Tunnel Tree. The yellow line marks the most star-studded path through the upper grove, including the Faithful Couple, the Clothespin Tree, the Columbia Tree, the Telescope Tree, the Fallen Wawona Tunnel Tree, and the Galen Clark Tree. The big blue "i" marks the site of the grove's museum. The partially hidden "P" marks the parking area. If the lot's full, you won't be allowed to drive to the grove; instead, you can park at the Yosemite entrance (see the "Ranger Station South Entrance" marker on the map) and catch a free shuttle bus to the trailhead.
Wawona Point provides an overlook of Wawona Meadow, which is partly visible at the northwest corner of the map. It's a worthwhile detour if you've got the time and energy.
The Mariposa Grove is just inside the park's south entrance. If you scroll to the southeast, you'll see the map turning gray, an indicator that you're outside the park (or your cursor is, at any rate). There's a trail, unmarked on this map, from the Goat Meadow Snow Play area to the grove, so you can see the grove for free if you're willing to hike several miles for it - and more power to you, I say. There's also a trail that is on the map leading from the grove to the Wawona Hotel.
The trail climbs steadily but for the most part not steeply throughout its course, summiting at the Fallen Wawona Tunnel Tree. If you're not healthy enough for a hike, you can buy a ticket for the tram tour, which will take you through both the lower and upper groves.
Alternative Map: The Mariposa Grove brochure, available at the trailhead for fifty cents or as a free PDF download from the NPS website, includes an arguably better map than this one.