This is the mother of all Yosemite day hikes, the ascent of Half Dome. Get an early start (like 8 a.m.) and pack plenty of food and especially water. Take the valley shuttle bus to Happy Isles (stop #16) then find the Mist Trail, which runs along the Merced River. After about 1.5 miles, you'll cross a footbridge that offers a view of your first stop: Vernal Falls. The trail ascends to the top of the 317-foot falls, then another footbridge takes you back across the Merced. The impressive Liberty Cap dominates the views in this area.
Soon you'll come upon spectacular Nevada Falls -- 60 stories tall. A series of switchbacks puts you at the brink of the falls. Signs at the tops of both cascades warn about getting too close; every year some unfortunate hiker gets swept over. You are now nearly halfway to your destination. Just above Nevada Falls, turn left at the junction onto the John Muir Trail, which runs along the Merced before retreating into the forest. You may be sharing this trail with some horse traffic, so be prepared to pull over.
About a mile into the woods, look for the Half Dome Trail on the left. (If you miss it, you'll eventually end up at the top of Mount Whitney in Sequoia National Park.) After another half mile in the woods, you'll emerge on a granite ridge that forms the top of the Quarter Domes. Finally, you'll get the back view of Half Dome. A ten-minute walk puts you at its base.
The last section of this hike is the hardest: you must pull yourself up by steel cable handrails set into the granite slope. Looking up at it, I felt just a bit of dizzying altitude sickness. I took a few minutes to catch my breath, then started hauling myself up. It wasn't so bad, as long as I didn't look down.
The summit was flat and large enough to hold a score of other hikers without feeling crowded. Looking west, the valley view was terrific (except that Half Dome itself wasn't in the picture). Looking east, the Sierras seemed endless. Looking down, it was scary with no barrier between me and the sheer cliff.
After about 20 minutes at the top, I headed back down the cables. (Be especially careful while passing other hikers.) The downhill return hike went faster than the ascent. I retraced the same route except that I remained on the John Muir Trail, which parallels the Mist Trail to the valley floor. It's slightly longer, less exposed and more woodsy.
In the woods, a fox quickly crossed my path. (A ranger told me that it was probably a young coyote, but I'm sticking with my fox story.) After about 10 total hours, 17 miles, and 4,800 feet up and down, I reached the Happy Isles bus stop exhausted but with the satisfaction of having bagged the valley's greatest peak.