I have hiked to the top of Half Dome twice, once in September 1996, and in June 2009. I didn't do any particular preparation either time; however, I was prepared for a long day hiking, and had reasonable fitness. If you've hiked in the Alps for 5 hours or more in one day you should be ready to tackle Half Dome.
You should prepare for the weather with appropriate clothing and planning. It won't be cold in summer months, but it can be very windy so take a wind-stopper vest or similar to put on when you stop for a break and at the top. Similarly, summer thunderstorms can move in very quickly, so you'll need a raincoat.
However, you must plan to allow for the weather. Arrange to have at least two days when you could make the hike, and pick the day you go according to the weather forecast. You must plan to be make it to the top and be off the summit before any thunderstorms arrive. On my second trip, we were just starting down when it began to rain, with thunder and lightning coming soon after. Later, I heard a rumour that a hiker had been struck by lightning on the summit and killed that afternoon. (If you have enough energy for two big hikes, I recommend the hike to the top of Yosemite Falls on your alternate day, as it has good cover so lightning is not a major risk, except for the very top.)
As well as picking a day with a good weather forecast, plan to start early. At my reasonable hiking pace, and stopping plenty of times for photos and to rest, I took 11-12 hours each time, starting from and returning to Curry Village. Aiming to start at 6am is a good bet. (Some very fit people travelling light start at 3am and make it to the summit in time for sunrise, so that could be an option as well.) Whenever you start, carry a headlight so you'll be able to hike in the dark if it comes to that.
Naturally you will need good hiking boots; the most uncomfortable part for many people is the hike down, where a proper fit is most important. For the cables, bring tough gloves as well; I used bicycling gloves with leather palms, which worked quite well. Yes, there will be inexperienced tourists, but not too many, as a hike that long and challenging requires commitment, and most people without hiking experience will be deterred. I think the risk of someone falling just in front of you is very slight. If it does happen, you should be okay as long as you are able to hang onto the cables with both your hands. The posts supporting the cables also provide a place to brace yourself.
But be prepared for the cables to be much more crowded than in the photo; I was stuck for 10 minutes while someone ahead overcame their fear and was able to continue. However, with the introduction of permits, the hike should be less crowded than I've experienced.
Rather than carrying water for the entire day (and taking it up the cables to the summit), I recommend a couple of bottles along with a water purifier so that you can fill them from one of the streams. Bring a sports drink to replenish electrolytes as well. Bring a good lunch and snacks as well, and ensure you have a good dinner the night before and a proper breakfast before you start or early in the hike.