Well I've only just started with this myself - but sometimes the best person to describe a new technique is someone who has just learned it, so I will share how I see it - but this is not an expert's view!
The basis of 'pressure and release' is to teach the animal to give in to pressure by rewarding it with release. This means that, for instance, you pull steadily but gently on the lead rope and as soon as the animal makes even the tiniest move towards you - even just a twitch of a leg, a slight stretch of the neck - you instantly release the pressure. After a short while you ask again - and maybe you get just a little bit more of a move towards you this time. Again, release the pressure. Then ask again. And so on.
Very quickly the animal learns that it need not fear pressure and that the way to reduce the pressure is to give in to it.
Some of the keys to success include never ever shouting or hitting, never raising your voice, always ask the same in the same voice with the same steady pressure. Always always always release the pressure as soon as the animal moves in the direction you want.
There are loads of practitioners who can help, loads of books you can read, several different names for the techniques.