DoubleS, there are some good answers here, but IMHO what you wanted to know was how to learn to perform a half-halt, and then how/when to use it.
First, it's 1/2 of a halt, and, you change your mind and drive the horse forward after the 1/2 halt.
A full halt should be these things ALL IN UNISON:
--your body stops following the motion of the horse
--you squeeze your butt muscles
(see jinx's video)
--you stop following the bit, as if you have become a pole and the reins are a lead rope.
Practice a FULL halt and master this FIRST. The is how to correctly "brake" your horse, like you use the brakes in your car.
The 1/2-halt is a pumping of the brakes...except you use it when you ride. You don't have to be a master of the 1/2-halt for the horse to accept it. I've been using a half-halt on my young geldings and they understood it very quickly. It has enabled me to change speed within gaits for several years now, and I used it on my older herds when retraining already broken older horses successfully. Later on, I used it to prepare for changes of leads, changes of footing (that I could see and the horse couldn't)--there are numerous ways to use the half halt to rebalance your horse, so learn it and practice it every time your ride and your horse will just get more responsive to it.
ANYBODY who owns/rides a TB can tell you that you have to use a half-halt to slow them down bc they must slow down through all of the gears--no slide stops for a TB!
Like Nike--JUST DO IT! Everything is awkward at first, BUT, you'll get better. The invisible half-halt happens when BOTH the horse and rider have spent hours and years together practicing it. Just didn't want you to get discouraged. =D