How to make my horse more collective/have a slower trot and canter.?

i ride at a professional reining barn, (my best friend won world champion 18 and under last year:)), but how she trained her mare to neck rein at the lope, she started at the walk, and got her to a point where she would collect when the reins were lifted, and when they relaxed, her nose would almost touch the ground. teaching to have that much submission to what the reins did, neck reining was easy, from there she moved on to a fast walk, then jog, trot, lope, canter, etc.