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I've climbed Half Dome twice, both times on July 4th (in 2017 and 2018). To prepare for the hike, I did a lot of stairs at the gym and outside, in addition to hiking long distances where possible (I was living in Alabama and had limited access to long hikes with significant elevation gain). I started with doing about 50 flights of stairs at once and ramped up to 250 flights over the course of several weeks. I felt more than physically prepared for the hike, including the difficult granite stairs at the base of the Dome.
For both hiks, I left the Pines campgrounds around 4:30 a.m. My group decided to take the John Muir Trail up instead of the Mist Trail because it's gentler on the knees and not as cold (the Mist trail can be cold if you get wet in the dark). We summited around 9 a.m. and spent several hours on the Dome enjoying the view and exploring all over. We took our time coming down, soaking our feet in the streams and taking in the views, knowing that whatever we would be doing in camp at the end of the day was going to be less interesting than what we would see on the hike.
(Additional preparation: you need permits for Half Dome. The Rangers will turn you away if you don't have a permit for each hiker. However, I have seen several folks get permits by waiting at the check point at the base of the granite stairs for parties that have extra permits, but this is not a guarantee.)