What I am going to write is not exclusively about starting to interact with a horse but something I am trying to do throughout my interaction with horses. However, it is especially important for me when beginning to establish new relationship dynamics with a horse who does not know this yet, which is why I am posting it here. The overall principle is to turn the interaction into something that makes sense from the horse's point of view, and then saying yes as much as you can.
For example, when going for walks with a horse, for some people this is a matter of preventing the horse from doing some things and making him do others. One side is the things they are trying to prevent from happening: to make sure the horse doesn't eat, that he doesn't push, that he doesn't stand still, or the other way around, that he doesn't walk too fast. So it's a whole collection of "DON'Ts". The overall attitude becomes one of preventing and avoiding, even when doing it in a way that is mostly based on positive reinforcement. You can also frame this as a collection of "DOs". Do walk on, do stay at the speed I have chosen, do this or do that. But again, I think this doesn't necessarily make it more fun for the horse. There still is a human who is trying to impose something on the horse which he considers important, while often ignoring or even trying to prevent the things that the horse considers important. It's a situation where one party is the influencer and the other one is the one being influenced.
I am sure that there are situations where this is necessary. However, I am trying to be very picky in recognizing these situations for what they are, and doing something else in all the other sitations. That "something else" is finding out what the horse is interested in and what he considers important, and then using this knowledge to turn our interaction into something that is directed at achieving these things. Thus, I try to create an environment in which it is in the horse's own interest to do the things I want, simply because they make sense to him and he wants them at least as much as I do. So my job is to frame the whole activity into moving towards
For example, consider a horse for whom the only thing he wants to do on a walk is eating but not walking on at all. He is planted there like a rock and the only movement he is interested in making is lowering the head to dive into the grass. It's one thing to prevent the eating and try to persuade him to move on, and when he does this, prevent the next eating, and so on. What works better for me, though, is to only make sure the horse doesn't eat but not to do anything at all to make him walk. Instead, I stand next to him and wait, and as soon as I perceive even the slightest tendency of him trying to walk into whatever direction, I do this faster than he can for a step or two, then bow down immediately and pluck a handful of grass for him. If he still is in a walking mood, I offer him to walk on (again into the direction that I know he prefers), go to the next grass and pluck that for him. If I see better quality food somewhere, like clover, I go there and offer this instead. In that way, suddenly walking has turned into something that makes sense for the horse himself - it brings him to the best grass.
For me that is different from just asking for something that makes no sense to the horse and then rewarding him for doing it anyway. This would be the case for example if I asked him to move on and then gave a treat for it. The walking would still be of little use to the horse because it is not in itself directed towards anything that is useful for him. He might even get annoyed, because after all he could also have had the treat much more easily without that stupid behaviour he needed to do for it.
So actually the principle is quite simple. In any given situation and for any behaviour of the horse, I try minimize the "DOs" and "DONT's" but find out whether I can see this behaviour as something where I can say "YES" to his own initiative, and turn that thing he wanted to do into something that is even better. You stop? Yes, I can do that with you and we will wait together (and then I am going to be faster in noticing when you want to walk on, and offer it before you can
). You want to eat? Yes, I can find the better grass for you! You want to run? Yes, and I am even faster, and I will run to the next interesting place with you! So it's all about not making things happen but instead creating an environment in which these things happen automatically, and then going with that. Makes my interaction with horses way more fun!