Dressage training is fairly common in ponyplay. While any pony will benefit from some aspects of dressage, most dressage training in ponyplay is specifically engaged in by show ponies or even dedicated dressage ponies. Thus, most dressage work in ponyplay is considered to be specialized training just as pulling a cart would be considered specific to cart ponies. Of course ponies can be cross trained in several disciplines. For example the ponyplay version of eventing includes dressage, jumping, and cross country just like the bio-equine equivalent.
Once a pony has mastered the basics such as walk, trot, and canter, then s/he should learn how to "move" at these gaits. This is especially important for show ponies because they will be partially scored for how they look at each of the gaits being judged. A ponyboy or ponygirl should show good impulsion at each gait; that is the pony should be moving freely and energetically and should not look sluggish or require too much urging to maintain a constant speed. A ponyboy or ponygirl should also be "on the bit." For human ponies this translates into acceptance of the bit (the bit should rest comfortably in the pony's mouth, and the pony should show no resistance to the bit's action (such as biting down on the bit or otherwise holding the bit with their teeth) nor should the pony be playing with the bit) and a nice high head carriage (the pony should always be looking straight ahead to where s/he is going, and should avoid looking down). The pony should be confident and balanced in her/his gaits and should show little hesitation in movement.
There is also the matter of extension and collection at each of the gaits. Extended gaits are those in which the pony is engaged and taking very large and long strides, lengthening the stride as much as possible. There should also be a good amount of suspension at the extended gaits. Collected gaits also require the pony to be engaged, but the stride length here will be very short (the strides should be the shortest possible at a given gait), with the pony instead taking much higher steps. In the collected walk, trot, and canter, the pony should be very light, with short, high strides. Look at a picture of a horse in extended trot and collected trot to get an idea for conformation and stride length.
Tempi are simply a series of flying lead changes occurring every one, two, three, or four strides. That is, for a pony cantering by putting one leg forward, then bringing the other leg forward to meet it, a flying change would be to change the leg that is moving forward first. A cantering pony should always have the same foot leading, unless he is being asked for a flying change. When a pony's trainer asks for a flying lead change, the pony should then commence using the opposite foot to move forward first and continue using this foot until asked again for a flying change.
For example, a pony being asked to do ones will change his lead every stride. If you watch a bio-equine do this, he looks like he is skipping along...it actually looks pretty amazing.
Passage is a highly elevated and extremely powerful trot. Passage is relatively easy to perform in ponyplay, more so than in the bio-equine world. A pony performs passage by raising his or her legs higher than in a normal trot and keeps each leg suspended in the air for a longer period of time. A passaging pony should look almost as though s/he is floating off the ground. The pony should appear to be moving in slow motion. A pony should appear very light and powerful in passage.
The piaffe is a highly collected trot where the pony should be trotting in place with no forward motion. The pony should have a clear and even rhythm to the trot with the legs being lifted up high and kept in the air for a period of time just as in passage. However, unlike passage, piaffe should involve little or no forward movement.
The pirouette is (typically) done at the canter. It is a very small circle at the canter, and should be in, or nearly in, place. The pirouette is best taught by making progressively smaller circles at the canter (whichever lead) until the pony is circling in place at the canter.
The half pass is one of several lateral movements in dressage. During the half pass the pony will move forward and to the side in equal amounts. The pony will be flexed in the direction of travel. Consider the case of your pony in a rectangular arena: while the pony will ultimately travel a diagonal path across the arena, his body will remain parallel to one side of the arena as he moves forwards. One way to think about this is that the pony will cross his legs as he moves (and faces) forward. Thus, if the pony is executing a half pass to the left, he will bring his right forward and cross it over his left leg such that his right leg is now both in front of and to the left of his left leg.
Side Pass (Full Pass)
Similar to the half pass, the side, or full, pass is a type of lateral movement. In contrast to the half pass, however, the side pass does not have forward movement. You can consider a side pass to be a half pass without any forward motion. Therefore, you will start the side pass from the halt and ask your pony to yield to your leg/whip without moving forward.
Start at the halt. Flick your whip on the pony's right side (your whip will emulate the action of a rider's leg) and maintain sufficient rein contact to contain any forward movement. Your pony should move sideways to the left, yielding to the leg pressure on his right.