Teaching a horse to lunge is a very important part of a horse's training. It teaches a horse to listen and respond to verbal commands as well as your body's visual cues. Also, by lunging a horse both to the right and to the left, you are exercising both sides of the horse's brain.
Start with just a short lead line and a riding crop and stand facing the horse's left shoulder. Hold the line in your left hand and the crop in your right.
Gently coax the horse to walk by stepping to the right so that your body is behind the horse's shoulder, tapping the horse's rump softly with the crop and saying "walk". Continue to encourage the horse to stay at a walk with your voice and, if necessary, small light taps with the crop. Only prompt the horse with the crop if it fails to keep walking.
Keep the length of the lead line very short to start with so that the horse is walking around in a circle very close to you; this way, you have more control over the horse. The end of the crop should be kept low to the ground as its height off the ground will eventually be used as a visual cue for the horse to know how fast to go.
If the horse begins to go faster than a walk, gently shake the lead line and command "walk" in a calm voice.
When you want the horse to stop, step left to its front, lower the end of the crop and command "whoa". If the horse does not stop, gently shake the lead line and repeat "whoa".
When you are ready for the horse to go the other way, make sure the horse is at a stop. Switch hands with the crop and lead line and gently pull the horse to the right, coaxing it with the crop to go the way you want it to. Eventually, you should never have to actually touch the horse with the crop or lunge whip when lunging it.
Repeat the above processes rotating the horse between going to the left and to the right. Be sure that you don't get into the habit of switching directions every time you stop the horse. Horses are very smart and can easily assume that you will have them turn every time. If you continue, the horse will eventually turn itself without any coaxing from you and "lunge itself".
As the horse gradually begins to understand the lunging process, you can begin to give it a little more room on the lead line.
When you are ready to teach the horse to trot on the line, give the command "trot" and raise the end of the crop a little more off the ground. You want the horse to respond to your voice and the height of the crop. Be sure that the horse has been trained enough on the walking part of lunging so that you are able to give them enough line in order to trot. The entire length of a standard lead line should be enough for this.
Canter and gallop can be taught to a horse in the same way with the verbal cues and the height of the lunge whip. These two should be learned on a lunge line so that the horse has adequate room to run.
Always remember to be patient and calm when teaching your horse new things, and try not to teach too much in one session or day. It will take much repetition for your horse to learn something new.