Well, the first thing to start on is a good 'whoa'. I good stop.
Your horse has to be collected, and stopping with his back end not his front to do a sliding stop.
My horse stops if I breathe out heavily. I don't need to touch the reins and I don't need to move in the saddle. By breathing out heavy, he drops his hind end into the ground. Work on that at a walk, then trot, lope and canter.
Next is collection - it will take a LONG time. You have to learn how to collect your horse and your horse has to be in good enough condition to basically do everything from his back legs. A reining horse is very light on the forehand. I'm sure you've noticed that with spins and the like.
Work in patterns, figure eights with lead changes, work on different speeds. Work on controlling your horse completely from your legs and your body position and breathing. A reining horse shouldn't need any rein contact during the entire pattern. Work on a lot of bending.
There is a lot to do to teach your horse reining, but the most important aspect is the 'whoa' in my opinion. Next is collection - like I stated earlier, a reining horse does everything by using his back end. He has to have his hind quarters engaged at all times, even while stopping. Then work on patterns and speeds. After you get the basics, it's fine-tuning from there.
Spinning may be the hardest. A rolling spur helps distinguish between cues. I roll a spur up the side of my horse lightly and he knows he is to be spinning.