The cables on Half Dome turn a class 5 rock climb into a class 3 scramble up the NW shoulder of Half Dome. This is by far the easiest way to get up Half Dome, but also the longest. Expect crowds on the weekends and even during the week. On busy days the cables turn into a continuous traffic jam of people. To avoid this problem see the "How to Beat the Crowds" section below.
This hike starts in Yosemite Valley at Happy Isles on the far SE side of the valley. The road to Happy Isles is closed to private cars. You have 2 options for this: 1) You can park at either Curry Village or the TH lot (continue east on road until the "busses only" sign and take a right on the dirt road leading to a large lot) and hike to Happy Isles on an easy trail that parallels the road, OR 2) You can take the free shuttle bus from almost anywhere in the valley, which will drop you off right at Happy Isles Spring through Fall. If you are hiking from Curry Village, it adds 3/4 of a mile each way, and from the TH lot it adds about half that distance. When the road starts to turn North, look for the trailhead on the right, immediately after crossing the Merced River. Another possibility is to ride your bike from one of the campgrounds. Thanks to bearbnz and snwburd for the extra info.
Once you make it to Happy Isles, follow the John Muir Trail on the North side of the Merced River, cross the bridge, and you will arrive at the fork for the Mist Trail about a mile after Happy Isles. You can either take the JM trail or the mist trail. The mist trail is more fun and a little bit shorter, so I recommend this. Follow the Mist Trail past Vernal and Nevada Falls for about 1.4 miles where it meets back with the JMT (or the JMT for 1.9). This is the last reliable source of water, so if you need it, hike about 100 yards back on the JMT to get to the Merced River above Nevada Falls. From the fork of the MT and JMT, follow the JMT for 2.5 miles through forest to get to the fork with the Half Dome Trail. Take a left and follow it for 1.5 miles to the base of Half Dome's shoulder. The switchbacks start here and in .4 miles you arrive at the saddle beneath the cables. This is where the fun starts (if you've managed to avoid the crowds). Take some gloves from the box if you haven't brought your own. If the cables are up. Just grab both cables and haul yourself up using the boards to rest. If the cables are down, meaning the posts and boards are out, you can just pick up one of the cables and pull yourself up. The cables last about 200 yards and reach a max slope of about 50 degrees. Once on top, enjoy the views and take a picture on the overhang (this is not "the Diving Board", which is on the Dome's SW side, but it still looks like one). The actual high point is near the overhang. You could start a game of football on top if you brought a ball. The summit is very large and more or less flat. When you're ready to descend, hopefully the cables are clear enough. If there are a lot of people, you can go on the outside of the cables, though a little more dangerous. Back track the way you came. On the way down, it may be easier (and dryer) to take the JMT instead of the Mist Trail. If you started late, it may be dark by this point. When you're back at Curry Village you can enjoy a pizza. Total mileage is 16-17 miles depending on your route, including to and from Curry Village. +5,000 ft, -250 ft one way.
Lots of water or water purification, warm clothes for the summit, gloves, flashlight (if you start late).
How to Beat the Crowds
If you are looking to get away from the crowds, Half Dome may not be what you're looking for. But there are a few ways to beat the crowds on Half Dome.
1. Go before or after the cables are put up (Before mid-May or after mid-October). The cables are still usable. Just pull yourself up with one of the cables.
2. Go during the week
3. Start early, probably before 6 AM. You'll catch the crowds on your way down.
4. Start late, after 10AM. This is what I did. If you're a fast hiker, or don't mind hiking in the dark, this is good. You will see a lot of people coming down, but you'll have the top to yourself. (we were there at 4:30, and there were only a dozen or so people. Depending on the time of year, you'll probably be in the dark by the end.
5. Do a night hike. I'm sure that sunrise from the top of Half Dome would be cool.
6. Do Snake Dike in Winter.
If you have information about this route that doesn't pertain to any of the other sections, please add it here.