I know there are several natural horsemanship techniques and I'm sure there'll be many to post up those ideas for you on here.
But I've reached a lot of those same goals with foals and adults through the use of positive reinforcement training. This style of training gives you the ability to say "yes" when the horse does what you want. It doesn't rely on making the animal uncomfortable or afraid to get the results you want. It uses little to no pressure (depending on how you choose to train, whether you want to shape the skills with saying "Yes" until they reach the goal you want - like the hotter and colder game with children or if you want to use pressure to persuade the right answer out of them.)
The reason I opted for the positive reinforcement training over typical pressure and release (well there are many), but one big one was, with pressure and release if you want the skill to get bigger (ex: going from walk to trot) you need to increase the pressure - while with positive reinforcement, the horse wants
to do the right thing so much that they'll increase their own criteria to get their reward. So when I taught my horse to walk on the lunge, walking faster got her a reward, so trotting must be better! I never needed to increase the pressure to get that trot out of her, she increased her own criteria.
When teaching my pony to jump, when he just trotted over the jump he didn't get his reward, but actually jumping did, now we're working on fine tuning his jump, getting nice and round.
I've found with this training style my horses are eager and willing to work for me, almost everything we do is completely at liberty, unless they're learning how to respond to particular pieces of tack.
It helps alot with nervous horses helping them overcome their fears, rather than by making them ignore their instincts to fight or flee, rather than making them work for being afraid, this method actually changes their opinions about new objects. It also works on a wide scale. For example, I spent a day introducing funny new things, tarps, plastic bottles, hula hoops (that have the noise thing inside) and all, I rewarded her calm curiosity, I had her target these new objects with her nose and stand on them and be rubbed by them, all the while rewarding her calm curiosity. By the end of the day her overall confidence was so much better, the first few objects took 10-20 minutes to work through until she was completely ok with them, but the last few objects took no time at all. Now when she's afraid of something she'll pause and if I have her target it or have her interact with it it's as if she goes "ohhh it's just another silly thing mom's showing me".
If you're curious about more of it here's a good link: Clicker Training: Challenge Accepted
Here's a pic of our most recent training session :)