One of my spinning buddies is tackling it in August & our instructor did it last year. It's a tough hike. The primary route up is on the trail next to Vernal & Neveda falls. Steep, rocky & usually wet trail. The final ascent is up a very steep granite slab. You hang on to a metal cable & use it as a handrail. Everyone says coming down is worse. Most come down the cable backwards rather than face down.
This is not a good hike for an inexperienced hiker. There are many spectacular hikes in Yosemite that are safer, but challenging.
The Half Dome hike doesn't require special gear just good hiking boots, a good daypack w/ a hip belt, & the 10 essentials. Get those boots asap & break them in.
Training? Endurance type weight training. I find step-ups the best training for hiking. Your hip flexors are going to work hard. Cardio wise, ideally you're hitting a hilly trail at least twice a week. You need endurance work - hours of moderate intensity. Video workouts? Probably BodyMax because it's so long & Interval Max because hiking is intervals.
A group from my Spinning class is hitting the trail frequently. We do a fast, hilly 3 to 4 hour hike. No whiners allowed. Sore hip flexors is the most common after effect.
Debra