I don't think there is an exact way to instruct someone to work with a wild horse. You need to see what is going on between the horse and handler before you can give specific directions. Every horse/human relationship is different. I've accumulated some thoughts and suggestions from my experience with wild horses in hopes that anyone working with a wild or unhandled horse will be able to get a sense of how the process COULD work and perhaps how "to be" when working with a wild horse.
I have two very important things that I consider when I first get into a pen with a horse. Number one I won't get hurt, and number two I will try to keep the horse from getting hurt. Safety first. Don't be a hero nor try to push a point that is beyond what you and the horse could accomplish. You don't build a house with the roof first. It takes a lot of small steps to get the entire house built.
Remember, if something is not comfortable for you, it's not comfortable for the horse either. I suggest you go observe as many different trainers as possible. Learn from each, then find what works for you and the horse. Every horse and person is different and learns differently. If you are not comfortable physically and mentally with what "Joe Teacher" advocates, it will be very hard for you to be successful in conveying that method of teaching to the horse. Find what works for YOU. Then massage and reconfigure it for each horse.
Probably the most important thing to consider in working with horses, especially wild horses, is that a horses needs to be able to move in order to learn. Being confined in some way, i.e. forced into a corner, squeeze chute, small space or tied up, just adds panic to the situation and instead of learning and thinking, the horses goes into flight mode and his brain shuts down. His feet need to be free. In his world, that is what saves his life. Remember that everything you do with a horse has to do with his feet, whether it is loading in a trailer, crossing a creek, doing a side pass or standing still. It's the feet.
Most of what I do is based on pressure and release/relief. I start a wild one by getting the horse to move both directions at my request. I do that by applying "pressure" to the horse. The pressure could be that I take just one step toward him. I use ONLY as much pressure as it takes to get the horse to move. Once he STARTS to move or even THINKS about moving, I release the pressure. I release on his try or better, his thought.
I'd like to see the movement smooth and with purpose: No bolts or quick stops, starts or turns. At first you may have the quick movements, but eventually, by releasing when the horse gives you the response you are looking for, he will smooth out and begin to understand what you are asking. By moving the horse and directing where his feet go, I can start to be a leader for the horse. Something most wild or "lost" beings look for - leadership and security. As in horse herds, there is generally only one leader. That leader commands his "post" by moving the other horse's feet. Directing them out of his space, over to water, away from danger, away from his feed, etc. Consistent, prompt, direct leadership.
You have to remember that the wild horse has no clue what we are asking, nor that there is an "answer" to what we are asking. Once they get the idea that there are answers to this "pressure", then things fall into place and the horse has "learned" to learn. Then the learning process picks up and when you ask for something the horse quickly looks for an answer. Again, here is where we need to recognize the thought or try.
Horses are very subtle animals. Generally speaking their actions are not big and bold. Usually it is a small change of posture (thought or try) that alerts another horse or you to an upcoming change or action. As I am working the horse I look for minute tries that says he is looking to "get with me"... it could be that his body rounds and changes shape (thought), in an arc like the round pen. His nose will dip in towards me (try) or maybe just the inside hind foot will be set under his body more than before (try). Those are all subtle tries. When he gives me those tries I will release the pressure by softening my body. I may slow my feet, stand softer (not erect) or change my thoughts about what we are doing. I was thinking "move on" and then when the horse responds by moving on, I think "ahhhhh good". Being that horses are incredibly intuitive, most of them can read your change of thought and they will react or feel release accordingly.
Horses are amazingly sensitive and astute to our intentions. That is how they live. They feel “stuff” as opposed to consciously thinking about “stuff”. So in dealing with them humans need to realize that horses probably know what you are going to ask before you ask it. The example I always use is that when you have a horse that is hard to catch and you head to the pasture to catch him, he is definitely moving away from you as soon as you start out. BUT... if you head to the pasture intending to fix the fence (even if you have a halter/lead on your arm) that same horse will come help you fix the fence. Intentions. Another example is while driving down the freeway, look at the person in the car next to you, he pretty much looks right back. He could “feel” you. Horses have that same sense, only greatly intensified.
Horses are not people. They don’t analyze things like we do. They are simple. I find the more “stuff” we take into the training realm of horses the less efficient we are. Because as people we have been taught in 1-2-3 order to do things and hence, stop and think “I have to do this first, that second, etc. etc.” If we get rid of the “I have to do it in 1-2-3 order” mentality of humans, we can do better with horses. Horses are “for the moment”. It’s how we present ourselves to the horse at that very moment that counts. So if humans are concerned about rules and regulations, we can’t clearly communicate with the horse. It’s OK to have that education, or call it boundaries, but don’t try to go step by step. With horses you might have to start at step 7 instead of step 1. And that is perfectly OK. Just be sure the responses are consistent and well learned before going on to the next lesson.
We live in a fast-paced, button-pushing, instant-result world. Horses are not "fast food". We need to take our time, be consistent and positive in the direction we want the horse to take. Most importantly, when we get even a small part of what we ask, RELEASE THE PRESSURE. As the horse learns, we can ask for more precise answers. Progress is vital to training, but take it one step at a time.
Above all, have fun. Gentling a wild horse should not be a job with a deadline. Take each positive as a huge thumbs up! You are working with a wild animal. Take a deer, put it in your garage and try to touch it. You have the same thing with a wild horse. But the difference being is the horse is truly interested in the relationship with the human. It is pure pleasure when that wild animal allows us to touch it. Or better yet, reaches out to touch us.