Ok, yes I did misunderstand! When I had been riding for only two months I was more worried about posting diagonals than anything else so it seemed very odd that you would be working on such advanced concepts.
Centered riding is a very good book to be reading. A lot of the visualizations really help to develop an effective and correct seat, which is the first thing you need in a half halt.
I was just at a Symposium with Christoph Hess and he kept nailing home the fact that the most effective aid is a correct position! This is not a new concept. When you are balanced and your seat is centered and correct - this will help to rebalance your horse. It is a passive aid, like contact, like the breathing leg, etc..
As far as explaining an active half halt, it is basically like the passive half halt which is applied by a correct position every stride, but stronger. You are basically slowing down the front end, while scootching the hind end under, while doing this the horse must maintain the contact. This means that the most your hands are going to do is feel extremely slightly in the fingers to keep the mouth soft, as they would anyways. From there it is about your body position adjusting to give a more active driving leg aid and a more active stalling seat aid. Basically you want to close your body around the horse while silling up straight. The best way that I've found to think about this is to put your elbows to your hips, swing more through the hips in the saddle while sitting in hard and closing the leg. In order to really apply an effective half halt, you need to be coordinated and have enough feel to apply these aids in the right order in the span of about a stride. It is a very advanced concept and the best way to learn it is to feel it without overthinking about the application, which is why you very very rarely will hear an explanation of the half halt. It usually interferes with the learning process.
The best thing you can do is go out and guinea pig it if you don't have a coach that can explain it. My coach lives 4 hours away from me and I live by videotaping myself and critiquing it inbetween lessons, and then videotaping those lessons to compare.