- Pressure in front of the cinch means move the front end
- Pressure behind the cinch means move the rear end
- Pressure on the cinch means move both ends (side pass)
Of course different disciplines and different trainers have their own variations, but those are generally used in western riding. As you get more practiced and the horse learns, the cues get closer to the center (cinch area) and less noticeable to an observer. They will start to respond to your leg pressure, rather than the heel, and the heel becomes a punishment, rather than the cue.
Start, as was suggested, by working on the ground. I start by using the handle end of a training staff or even something like the handle of a hoof pick, to give the horse a cue to move the part I want him to move.
Say, for instance, I want him to move his hind quarters away from me. I will poke or pressure him lightly in the belly, about where my heel will be while in the saddle giving the same cue. If no response, the cue gets a little harder. If no response, the third time the cue gets very uncomfortable and generally the horse will move away. I hold his head with the lead at first, so that he has to move his rear away. Ah! Reward time! Release pressure, a couple pats, then the light signal again, etc. After just a few short minutes, he'll get the idea and I can then move to another cue and start working that. This is the time you'll also want to start teaching how to move his feet properly. The foot next to you should move across in front of the far hoof, not behind and not next to. As he learns the cue to move, start keeping up the cue until he moves correctly. You have to teach every thing on both sides, because a horse doesn't necessarily relate things to right and left sides as we do.
Teach him how to move on the ground, so that when you are in the saddle all he has to do is figure out the cue.
After a couple of days of working on that, along with other ground training, he'll understand the cue enough that when you are in the saddle and give him a heel, he'll figure out pretty quickly what you're talking about, and he'll already know how to do it. You may have to hold his head at first with the reins.
Now the trick is to practice these cues until he does them with a light cue from the saddle. After he understands the cues, and you know he does, and you know you are giving the cues in a consistent and learned way, the way to get him to respond to a light cue is to give him the light cue, then the second time make it very uncomfortable for him. He will learn to respond to the light cue.
I find spurs to be very helpful in training leg cues. However there is a correct way to use spurs and there is an abusive way. If you do not know how to use spurs, I would suggest you put some on and ride a calm horse that does not need them. It will help you become aware of how you use your heels, so you don't inadvertently jab when you don't intend to. You also need to get your green horse used to them before you start jabbing him with them, or you may get a big surprise!
In my experience, horses learn more quickly, try harder, and are more willing students when I wear spurs.
Another thing, a bit is only as harsh as the rider's hands and the horse's obedience (or lack thereof) make it. A horse that is obedient, with a rider that has "good hands" doesn't have to worry about a bit. Some bits actually help keep a horse's mouth wet. Some bits have metals that actually taste good to a horse. Some have "crickets" that a horse can tumble with their tongue to reduce nervousness. Still, I've seen horses that have learned to distrust a bit, or that a bit in their mouth means it's time to race, and a bitless bridle works better for them. A hackamore is just as mean as a bit in the hands of a novice or on a disobedient horse.
Most trainers I know start a horse in a snaffle bit, then, after the horse learns what to do and has a basic understanding of what is expected and is obedient, they progress to a hackamore with a rawhide bosal for a while, to refine the horse's responsiveness, then comes the bit for the finishing touches.
I have no use for a mechanical hackamore, although my dad likes them for everyday riding.