Hike to half dome...one question is if you hike regularly? If you do, then you might be able to do the day trip hike. But definitely camp in the valley, start the hike at sunrise or even before. The hike to the aforementioned "waterfall thingy" I'm guessing is Vernal Fall, which is quite an easy hike.
What you'll probably want to do depends on what time in the season you go in. If the water is still high then you're probably better off taking the John Muir Trail so as you don't get drenched in water early in the morning. But if the water is low then you can cut some time and mileage off by taking the Mist Trail. And that's where the trail starts getting harder. The Mist Trail is built out of stone steps, levels off, and then goes into steep switchbacks. Once you reach Little Yosemite (which is where you would camp if you make it a 2 or even 3 day trip) it levels out for a while until you split off to Half Dome. It switchbacks up more and gets steep when you get to the sub-dome part of it. At the saddle between the sub-dome and the actual Half Dome you drop your pack and pick up old work gloves (if you didn't bring any) and go up the cables.
"The cables are to help keep your balance, you don't pull yourself up just by the cables, but walk along them, holding on to keep your balance on the steep incline. It's kinda like a steep staircase, but the only stairs would be the metal ties used to secure the cable poles to the rock. "
Well this isn't entirely true. If it weren't for the cables, this would be unclimbable without being a total rock climber. Slick rock, 45+ degree angles, and exfoliating granite you go up and over makes it very difficult. You do pull yourself up, with the cables suspended above 2x4s every 6 feet or so.
I myself have never done the hike, many other hikes in the Valley, but never up to Half Dome. If you want to do it in a day, I would not reccommend it if you aren't used to hiking. If you want to do it in a couple of days, I would not reccommend it if you aren't used to backpacking. Not sure of your abilities.
If you're interested in Yosemite too, just went there and there's a trip report here