When you first start teaching a horse to heed, you use a corridor of aids or pressures to create a feeling in the horse of where you want him to move. As the horse's understanding increases, the handler can not only change the direction of the horse's strides but also their length, speed, and cadence.
Longeing in a circle falls into the category of advanced heeding for several reasons. First, the horse and the handler are working in a corridor at a distance from one another. Second, the handler is no longer doing simple, basic heeding with his or her primary line running parallel or perpendicular to the horse's primary line. The horse no longer just mirrors the direction and speed the handler is moving. And third, it is difficult to create a full corridor of aids that create the exact feeling of a circle.
Before you start teaching your horse to longe, he should understand that when your primary line (an imaginary line running in front and in back of you and parallel to your spine if you were on all fours) is behind him, you are following or chasing and want him to move forward away from you. He should understand that when you put your primary line on or in front of his secondary line (a neutral line running through his withers and perpendicular to his spine), that is a block of his forward movement which means "stop." He should be comfortable heeding at the walk and trot in both directions while being handled from either side. He should understand that when you swing your primary line out away from him or in towards him you are indicating that you want him to turn in the direction you are opening up or closing in.
Once he understands all that, you are ready for longeing. You first establish the feel of a circle by heeding him in a circle, continually opening your primary line to the inside to keep him turning. In the beginning, you can use the walls near the corner of the arena to help you create this feeling. You can also use a round pen. Round pens make teaching longeing easier because they help create a circular corridor of pressures.
When the horse develops a strong feeling of a circle, you can start heeding a little farther out from him. As you move out away from the horse, begin gradually dropping back toward his hip in a following motion. As you approach the center of the circle, swing your primary line so that it is behind the horse's withers. This continues giving the horse a feeling that you are following and want him to move forward. You can fuss a little with the longe whip to move the horse forward but the most important driving aid or pressure is the position of your primary line. Exactly where you put your primary line behind the horse's withers and how quickly the horse understands the direction and speed you want him to move is going to vary from horse to horse and handler to handler.
It is important to set right mood and establish rhythm and relaxation in the horse before you start moving away from him. Then maintain that rhythm as you move into the center of the circle. Briefly position the horse's head with your longe line then soften, position and soften, position and soften. This prepares the horse later for the feeling when he's ridden that the inside rein indicates where you want him to position his head.
You want to establish a circle and then create a steady rhythm that mesmerizes the horse. Anytime you use an aid or a pressure that doesn't match the rhythm, you interrupt the rhythm. It's the steady rhythm that maintains the circle, not a steady pull on the longe line. Don't hold his head and pull him toward you to keep him on a circle. A constant pressure on his head masks the feeling of where you are and spoils the corridor of pressures you want to create. When you are working in a round pen, be especially aware of maintaining the horse's rhythm. Don't put so much pressure on him that he begins bicycling around the perimeter of the pen. You want rhythm and relaxation, not speed.
Some horses have a problem positioning their head to the inside, especially in one direction, because there is no full corridor of pressures directing them on the circle or because they may be stiff or weak on one side or the other. A round pen can help create a corridor of aids but it won't necessary correct the horse's head position if he has physical problems.
When you are heeding alongside a wall or fence and you want the horse to trot, you indicate this by taking bigger steps and making a little fuss behind you with your whip. Then when you want your horse to trot on the longe, use those bigger steps and a little fuss with the whip to help him understand you want him to change gaits. Similarly, prepare the horse for stopping on the longe by adding vocalizations to your stops while you are heeding along a wall or fence. Then when you are longeing, you can use a little "ho, ho, ho" along with moving your primary line ahead of his withers to ask him to stop.
If the horse stops on the circle and stays standing in the direction he was traveling, just walk up his neutral line, scratch a groom a little, then turn and start him off with a little heeding in the other direction before you drop back to the center of the circle again. The horse may stop and turn to face you, especially if you are using a round pen. Then just walk up his primary line, scratch and groom, then heed him in the new direction you want him to move off.