Half-halt in VERY simple terms: drive, squeeze (hand), release.
I was told by well-known trainers and Olympic level riders that the release is the MOST important part. It's the release phase that builds self-carriage.
These three bits are tiny adjustments, a little close of the leg or slight driving seat; a tiny closing of the hand (tightening the spring or the bow, if you prefer), then the release of the "spring".
The more highly trained a horse is, the smaller and lighter these things should become. The seat can become either ******ing or driving (whatever you need at the moment), the hand softens as the horse rebalances in collection, sitting more on the haunches and lifting the forehand.
When it's working right, it's a pretty cool sensation!