Well, half halting is not really just a "dressage thing" for lack of a better term. ;)
It's really kind of self-explanatory. You have the general gist. When I half halt, I sit deeply in the saddle, like I would when I do a full halt, but not quite as strong. I apply squeeze-release pressure on the outside rein. And that's not the only way one can do a half-halt - just check out google, I'm sure they have loads of methods. But that is what works for my pony and I. There is not a full down transition, rather, just the gait of the horse slowing down a bit and collecting - but make sure you keep your leg on so the horse doesn't loose the power either!
But half-halts are not just pulling on the reins a little. You should be reacting first with your seat. They are also used not only to slow the horse, but to also give the horse a subtle "heads up" that you are about to ask for something new. So if I am going to make a circle, a couple of strides before we get there, I just give the horse a little hint that we are doing something new, and usually the transition to the new thing is much smoother when the horse has some "warning".
A great exercise for practicing half halts, among many other things it will improve, is extending and collecting the trot. I will pick out certain points at which to extend or collect. So, at one place I will do a slower, collected trot. At the next point I might do a nice, steady medium trot. Then, at another point, I will go up into a faster extended trot where the stride is long and I have my horse really stepping out. And in all orders and patterns of this. When I make the transition from, say, my steady medium trot to slower collected trot, the half-halt is what gets me there for that. So that you make not a full transition, but a change in tempo of the current gait.
Cinnamon Whiskey 11 y/o 15hh Chestnut AQHA mare, 2'6 Jumpers