I am going to tell you what worked with my mare though I don't know if it is the 'correct' way of achieving long and low.
So my mare loves to be a giraffe, she trots really quickly and sticks her head up in the air and generally goes around rather tense and unresponsive. So I decided that long and low (and relaxing) would be a great thing to teach her. My mare doesn't like to be slowed down with rein pressure and doesn't like someone trying to pull her into a false headset with the reins so I approached teaching her long and low like this:
I kept a very light contact with the reins but held my hands slightly wider apart and lower down than normal - to try and encourage her to drop her head and go forward to seek the contact. And then I just started trotting her. And trotting her and trotting her. I regulated her speed using my seat but asked that she kept trotting and trotting (she wasn't allowed to go faster than a standard trot but nor was she allowed to walk). Eventually, she got tired or just happened to drop her head (and I made sure my hands went with her to allow her to drop her head freely) and the moment she dropped her head, I asked to her to walk (thereby rewarding her by not making her work anymore).
For the beginning few rides, whenever she dropped her head (even if it was two strides in which she quickly learnt to do) I would bring her back to a walk and allow her to relax. Once she started dropping her head almost immediately once asked to trot, I asked her to maintain her head low for a quarter to half of a circle and then rewarded her with walking (but only if she kept her frame long and low for that half a circle). Now I'm progressing to full circles with her and she really has changed her entire way of going.
Its just important, in the beginning, to reward often so they understand what you want from them. But that's just how I approached it so hopefully you can get something useful out of it.