How do you encourage your horse to want to be with you Assuming it is a horse that has not been handled much I put him in a round pen or small arena and let him go and do whatever he wants for several mintues while I'm in the pen. I'm just observing at this stage. After about 5 or 10 minutes I do approach and retreats and / or run or walk around at the same intensity as the horse does. Basicly mirror its movements. If he runs I run parellel to him and then quickly run the other way. If he is just walking I do the same thing but at a walk. I do this and progressively get closer to the horse until the horse's curiosity takes over and he starts following me when I turn away. I then offer my hand as I face him at an angle. If he touches it I pull it back and turn around. Once he touches it a couple of times I then attempt to touch the side of his neck to pet him. If he stands still great. If he moves off I turn around again and walk off. Eventually when he starts allowing me to pet him all over I then start attempting to have him move his head, hips, feet, etc with direct pressure or by just my movements.
When he is no longer reluctant or frightened by me touching him and asking for movement I can progress to more specific requests using a halter and rope.
That is a very brief explanation of what one can do. For the most part when you start asking for requests that cause him to move his feet alot will cause him to want to be with you more because you will come across as a strong leader who knows what you want.