Please know that permits are required seven days per week to hike Half Dome when the cables are up. Please see the NPS Half Dome Permit page for details. Anything they say there supercedes anything I say here.
Your first choice is to decide whether or not to do this as a day hike or an overnight. I have found a page on the net (now where's that link?) where the person says that most people regret doing it in a day. Personally, I would regret doing it as an overnight. His logic is that most people find it too grueling to enjoy if they do the round trip in a day. This has not been my experience and the Yosemite Mountain School hiking guides frequently take people up Half Dome in a day. My logic for not wanting to do this trail as an overnight is simple. This is well within my fun day-hiking distance and I don't really want to go backpacking on such a crowded trail. If I'm going to hump all that overnight gear somewhere, I want a wilderness experience and the fact is that the Half Dome Cables trail feels more like Manhattan at lunch hour.
If you insist on doing this as an overnight, you may have to choose a trailhead other than Happy Isles or Glacier Point. Quotas for backcountry permits are set on a per-trailhead basis, so it can be extremely hard to secure a permit for the most popular trailheads. The good news is that there are other options that add very little extra effort. The next easiest is to start at Mono Meadows. If you want more mileage, you could start at Tenaya Lake for a 22-mile round-trip hike. Not a bad option as you'll have chance at some solitude for part of you hike at least.
My preferred option is simply to get ready and get up early. Rickey Gates may have run this trail in in 2:28 round trip, but most people will want to get up early and get going both in order to have the full day and in order to get up out of the Valley before it gets too hot. Also, if you start early enough you will to some extent beat the crowds, especially on the first part, since a lot of people hike just part of this trail and start late. If you start before the shuttles start running (7:00am) and just walk to Happy Isles, you'll cut down on the amount of company you have on the trail.
Your first objective is to get to the top of Nevada Falls. Most people do this by starting from Happy Isles and hiking the Mist Trail or the John Muir Trail. Another option is to start from the Glacier Point and hike the Panorama Trail, but this option will leave you with the 1000 foot climb up from Illouette Creek back to your car at the end of the day unless you catch a ride or shuttle up to Glacier Point. I won't discuss that portion of the trail since I already have a detailed page on the Mist Trail and will eventually add one for the Panorama Trail.
From the top of Nevada Falls, you have a mellow and gentle hike with excellent views of Liberty Cap and the South Face of Half Dome. After about a mile along the Merced, you come to the mouth of Little Yosemite Valley, usually called simply "LYV", with its large and crowded campground. When the trail forks between the Half Dome trail and the campground/Merced Lake trail, you will leave the riverside and, consequently, convenient places to refill you water bottles. At this point the river has passed one High Camp, one stock watering hole, and one crowded campground. I rarely filter Sierra water, but I would recommend filtering here.
Little Yosemite Valley campground is the preferred campsite for overnighters. Despite the name, if you only go as far as the campground, you get little sense of why the spectacular Merced River Canyon merits being called "Little Yosemite Valley" — for that you need to hike at least another three miles toward Merced Lake, but that's for another page. I'll just note here that if you can get two nights at LYV campground, you could hike a few miles of the true LYV before heading out on your last day. On the down side, permits for the LYV campground are hard to come by and this is far from a wilderness experience. It resembles the hustle and bustle of the Valley campgrounds more than it feels like a wilderness site (full disclosure: I've never actually slept here, but I have hiked by in the evening and even as late as 9:00pm, so I have a sense of what it's like at night).
Once past Little Yosemite Valley, the trail will begin to rise again and become more forested with your typical mid-altitude mixed conifer assortment (Red Fir, Jeffrey Pine). At 2.5 miles from Half Dome, you'll pass your last signed trail junction where the John Muir Trail and the Cloud's Rest trails break off. A half-mile past this there is a spring where you can refill for a last time. The spring is easy to miss, but if you are low on water, keep your eyes open and focused on the left side of the trail and with luck you'll find it.
From here follow an increasingly dusty trail until the forest opens up and the shoulder of Half Dome comes in view. From that point, things get steeper and steeper and ever more spectacular until you get to the top.
Before reaching the summit, you have to confront the cables. These are steep and generations of hikers have made the rock rather polished. I'm amazed there aren't more serious accidents here, but there do not seem to be many. Nevertheless, in recent years there has been a rash of deaths here after many years without incident, so don't take this too lightly. The park service has a pile of old gloves at the base, but it's probably worth it to bring some work gloves that fit (though I never have actually).
Under no circumstances should you go to the top if you see clouds moving in. People have been killed here by lightning strikes. Also, never throw anything from the top — there are climbers below on the Regular Northwest Face route (and others) and you could easily kill someone.
Once on the summit, you will have awesome panoramic views of the Valley, Mount Hoffman, the Clark Range and the Sierra Crest. You yourself will be in a barren moonscape. Old photos show that this was not always the case, but we have loved the summit of Half Dome to death. There are still some rare Mount Lyell salamanders near the top, which is the reason for prohibiting camping up there. Still, the views are amazing and it's one of the best picnicking spots in Yosemite. With the crowds, there's often a festive atmosphere on the summit. Enjoy! It's a long trek back down.