Hike Distance: 14.2 miles (22.7 km) round trip via Mist Trail (the red line plus the yellow line)
16.5 miles (26.5 km) round trip via John Muir Trail (the red line, the green line, the yellow line, and a bit of the blue line)
20 miles (32 km) round trip via Glacier Point (the blue line plus the yellow line)
23 miles (37 km) round trip via Tenaya Lake (the purple line)
7 miles (11 km) round trip from Little Yosemite Valley campground (part of the yellow line)
Half Dome Elevation: 8,846 feet (2,696 meters)
Total Elevation Gain: 4,800 feet (1,600 meters) from Yosemite Valley
The red line marks the route of the Mist Trail, which will take you (if only! actually, you'll take it) to the top of Nevada Fall. This stretch is 2.6 miles (4.2 km) long and climbs 2,000 feet (600 meters). It's the most scenic stretch of the trail until you approach the shoulder of Half Dome. It's also the steepest stretch until then. The last few hundred meters of trail to the top of Vernal Fall are stairs hewn from the granite cliffside, and the trail from the base of Nevada Fall to its lip is a memorably long series of switchbacks. The pit-style bathrooms at the top of Nevada Fall are the last man-made toilets on the route unless you detour to the Little Yosemite Valley campground.
The yellow line marks the ascent from Nevada Fall to the top of Half Dome. This stretch is 4.4 miles (7 km) long and climbs 2,800 feet (850 meters). It starts with a refreshingly flat interlude through Little Yosemite Valley, with the Merced River off to your right. Once you turn north you'll begin climbing, and when you reach Half Dome's eastern shoulder and turn west again, the really steep part of the trail begins, starting with a series of switchbacks up the shoulder and ending, of course, with the perilous cable route.
The blue line marks the path of the Panorama Trail, which you'll take if you're starting from Glacier Point. This section of the trail is 5.5 miles (8.8 km) long and intersects with the main Half Dome trail above Nevada Fall. It has a net descent of 1,200 feet (365 meters), but since you descend from Glacier Point to the Illilouette Gorge and then climb out again, the overall elevation change is much higher. The trailhead is just offscreen to the west; you can click on the map and drag to the right to see it. Besides Glacier Point itself, highlights of this route include Illilouette Falls and the Panorama Point overlook.
The green line shows the Muir Trail alternatives to the Mist Trail route. This way is longer and less scenic, but also less steep than the Mist Trail, and worth considering on the return trip if your knees are showing signs of imminent mutiny. While the Mist Trail route is 2.6 miles (4.2 km), the Muir detour is roughly 3.7 miles (6 km) long. It's not free of switchbacks, but they are much gentler. Although the scenery doesn't match up with the Mist Trail's high standard, the top of the route does provide a remarkable view of Nevada Fall, Liberty Cap, and the back of Half Dome. If you return to the Mist Trail via the middle fork, you'll be coming out just above Vernal Fall. If you take the lower fork, you'll rejoin the Mist Trail (assuming you're on your way down) above the Vernal Fall footbridge, which is roughly half a mile downstream from Vernal Fall.
You can also hike Half Dome starting from Tenaya Lake, though it makes a very long day (23 miles/37 km round trip). It's probably best as a backpacker's route, with an overnight stay at the Little Yosemite Valley Campground. It's left off this map to keep Google Maps from zooming out to Plutoesque altitudes, but here's a version of the map that includes it (it's the purple line).
If you're starting from Yosemite Valley, as most hikers do, note the two big blue letter P's, which mark the closest parking to the Half Dome trailhead. The one on the left is Curry Village; the one on the right is the trailhead parking lot, which is closer but fills up early. If you're spending the nights before and after you hike Half Dome at the Upper Pines campground, which is just across the road from the trailhead parking, you can start from your campsite. The extra hike is also manageable if you're staying at Curry Village or the North or Lower Pines campgrounds.