Official Site: https://www.nps.gov/yose/planyourvisit/halfdome.htm
Hiking information: http://www.yosemitehikes.com/yosemite-valley/half-dome/half-dome.htm
Hiking information 2: http://www.yosemitehikes.com/yosemite-valley/half-dome/half-dome-trail-map.htm
As the iconic feature of Yosemite valley, Half Dome is the most popular destination for visitors to the park. At 8,800 feet above sea level however, reaching the top is no small task, with people dieing every year attempting the hike.
In order to hike Half Dome, you need a permit. To get a permit, use the official park site (https://www.nps.gov/yose/planyourvisit/hdpermits.htm) and sign yourself up for the lottery system. Most permits are awarded through lottery near the end of March with additional lotteries later on during the summer. Have everyone in your party and possibly even some friends who aren't going sign up for you to maximize your chances. We had six people in our party go and only one of us won a permit.
If you can't get a permit, a last resort option would be to hike to the base of Half Dome and attempt to join someone on their permit. Permits accommodate at most 6 people (I think) so smaller groups can bring up others if they feel generous.
For those of you who fail to get a permit and hate the system, understand that before the advent of the permit system, hiking the trail was so much more unpleasant due to overcrowding; especially at the cables. There were way too many people attempting the cable portion of the hike that shouldn't of, who held up everyone else for half an hour or more. Even today with permits, you'll still have people who can't complete the cable portion of the hike for mental or physical reasons that slow the entire ascent down.
I just believe that the permit system overall has made the Half Dome experience much more enjoyable. I mean the views are the same, but the need for permits keeps the trail manageable and it forces you to be more serious about planning your hike as you should.
That said, the permit only limits you to the cables. You can still hike a majority of Half Dome, so all is not lost. Personally though, I would be frustrated to hike 4-somewhat hours only to have to turn back so close to the Dome.
Planning the Hike
Before doing the hike, I suggest assessing your fitness level honestly. The Mist Trail is a tough hike. In total, The Mist Trail is 14.2 miles of switchbacks and sharp inclines under a relentless sun.
Most people who are serious about the hike leave their campsite around 5-6am in order to hike as much of the trail under shade as possible. Anyone who decides to leave later, say 8am, will have a much more difficult hike because of the sun and the crowd; the worst thing that can happen to you is getting stuck behind a long line of people and having to bake under the sun longer than you need to as well as being forced to move at an inefficient pace (slower than you normally walk).
On average, the hike takes about 10-15 hours to complete. To offset the Mist Trail steepness, you can alternatively hike the John Muir Trail which adds roughly 2 miles to the hike (16.5 miles).
The Mist Trail is well maintained, clearly marked, beautiful, windy, steep, and altogether challenging.
Don't be complacent at the pools above the waterfalls because...you know, there's a waterfall that can kill you if you swim too far.
Hopefully, the experience at the end teaches you something about yourself beyond checking off Half Dome off your to-do list.
Once you reach the top, there's a great place to rest with plenty of shade if you walk straight forward from when you exit the chain. There will be a set of "stairs" with a giant wall providing shade.
Oh yeah, don't leave food unguarded. The crows are bold.
I suggest bringing 3-4L of water.