A half-halt is basically just that - a little bit a "brake" but not enough to make them transition down. It is done by a light tightening of the outside rein, but continuing to push them out with your seat.
A half-halt can he used to slow the speed of a gait and can aid in adjusting the stride with help from the seat, but it is also very useful for other things. It lets the horse know you're about to ask for something, for example. It is used when asking for collection. And it is also used to encourage cleaner transitions, to stop the horse from running up into the new gait.
A good exercise to teach your horse this would be to start in the walk. As her to walk as fast as possible without trotting. Then, sit deep in your seat and put pressure on the outside rein, and get her to walk extremely slow. Then, ask for more speed. Wash, rinse, repeat. Always praise of course, and remember to use twice as much seat and leg as hand. Always!
When she starts to respond quickly and easily to that (she will probably pick up quickly on it), try it in trot.
Personally, I wouldn't canter with a horse who hadn't cantered with a rider before that hadn't been taught the meaning of a half-halt. She will probably feel unbalanced, and as a result, try to rush, and you will need her to understand the half-halt so that you can support her with it and slow her down as well.
Inside leg to outside rein will be key when the time comes though. Let her have her head so that she can find her balance easier, but don't totally drop her support! :)
Cinnamon Whiskey 11 y/o 15hh Chestnut AQHA mare, 2'6 Jumpers