Here is how I explained it in a thread to Kim W about 2 weeks ago - everytime I tried to copy the link to the whole thread, it also came up with access to my PM storage - how weird!!
Yu could search for the thread if you want.
OK I'll give it a try and maybe I can paint a picture for you - others can elaborate on it as I don't present myself as an expert. Also, I ride English and am not sure how exactly how to do this western style.
You teach the horse a one rein stop at all gaits before you ever need to use it in a real life situation. I start on the ground by teaching my horse to respond to pressure from one rein by flexing their neck so that their nose basically comes back to their barrel. You almost have to stand near their hip and gently pull their nose around, both sides of their body. I did this daily for a week with each lesson causing their nose to come back farther and easier. I also started with a lead rope and then went on to doing it with a bridle and bit and then added mounted with bridle and bit.
Then from the saddle - mounted but not moving - holding your arms bent at the elbow and close to your side - move your arm straight back next to your body so that your hand with the rein comes to your hip which also brings your horse's nose to his barrel/shoulder. At the stand still, he should flex/bend his neck but not move. I keep my legs loose - I don't want him going anywhere so I am not squeezing. Again, both sides.
At the walk, with my elbows bent and keeping my arms at my side, I draw my hand back to my hip (maybe a little in front of or a little behind my hip) again causing my horse's nose to come to his barrel/shoulder. If I put my arm out to the side, his head comes around but not to his barrel - I want a tight bend and not a graceful arc. Again, legs off because I don't want him going anywhere b/c I want him to stop. He may make small tight circles but he will eventually stop. It may take 8 or 10 circles or more to begin with (and you may get dizzy) but as you practice the circles will become less and the stop will come sooner. The idea is eventually that when he feels your legs off and your hand come back to your hip the stop will follow automatically.
Again practice from both sides. One hand is coming back to the hip and the other hand is staying up near the saddle horn or pommel or his neck and is keeping that rein loose. Sometimes when practicing at a walk I will "drop" the rein I am not using and just bring the one back to my hip (I ride English and the rein ends are connected).
Again the idea is that in a run away or bolt situation, the horse has become so flexible and conditioned to your one rein stop that he turns his head and follows his nose in a circle instead of running off with you. Or instead of into a tree with you or whatever!
Each time I ride I tend to do this just a time or two for practice and to keep it fresh and my horse responsive. I haven't yet had to use it in an emergency but I will say that my horses stop better and just in general are more responsive the more I get them to flex. I have used it in situations where my one horse tends to get flighty - i.e inthe arena with all sorts of noises and activity going by the door, rather than her taking off, I just immediately did the one rein stop to get her standing still and not reacting to all the commotion.
Oh - sometimes - just for something different I also combine the one rein stop with disengaging the hind quarters (the foot on the same side as the nose at the barrel steps over in front of the other hind foot so that the hips are loose and not all tensed up in a "run for my life posture" - and I also teach that from the ground and go over it once before each ride).
Was that the picture you were looking for or shall I try again?