I teach mine by doing a lot of circles and serpentines. Start by laying the outside rein against the neck just a moment or two before tightening the inside rein. Make sure that you aren't contacting the bit with the outside rein. Keep doing that and slowly start weaning away from the direct rein. Lay the outside rein a moment or 2 and if they don't respond, then correct with the direct rein. Don't keep the pressure on there constantly or they will become dull to the rein on the neck. My circles usually end up looking more like squares during this time in their training because I will turn them then let them straighten out, then turn them and let them straighten out over and over. It really doesn't take them very long to figure it out. Make sure that you reward even the smallest attempt in the beginning by allowing them to straighten out for a few strides. Just remember to not contact the bit with the outside rein.
This is a filly that I had 11 rides on (this is the second half of the video). I had been working on the neck rein for about 3 days and this is the type of pattern that I usually worked in. I would always mix it up a little bit and didn't follow a set plan of which way I was going to turn, I would just turn whichever way I felt like. I will usually keep them going one direction until I like how they feel. You can see at the very first where I reach up to correct her. Then a few seconds later, she was hyper-reactive to the cues (happens sometimes). Then in the middle, she started feeling a little stiff so I reminded her to bend and give to pressure. She always did better to the right so I spent a lot of time on the left.
I usually start from the butt and work up to the reins.
Make sure when you sit down, that means whoa. I make sure my horse knows how to move shoulder, rib, and hind quarters. Collect on spur pressure, if for show classes. Once a horse is soft in the body, I just start weaning away the rein. If the horse doesnt come around when I ask, I just show them.
I taught my TB the same way that smrobs did--over-exaggerate your direct reining while having the opposite rein laid up on the neck. However, I've also heard of the "criss crossing method" where you twist your reins around so that when you pull one way, the opposite rein automatically comes with it.