Most of the time in ponyplay when a pony is moving forward, especially at any gait aside from the walk, the pony is being driven from the ground either with the trainer following behind the pony, on a line, or on a cart. Thus I define leg aids as equivalent to whip aids for these situations. Obviously, if you are physically able to apply leg aids to your pony, then use your leg when possible. However, as I mentioned, many times we cannot use our actual leg, so in those cases, I will consider the whip or crop to be a surrogate leg.
The most common leg aid used is that when we want our pony to move forward. In this case use a flick of the crop or whip on the pony's lower back or ass. This will indicate we want impulsion from the pony. Thus, in conjunction with appropriate rein aids, this can also indicate to the pony to move backwards.
As a general rule, we want our pony to yield to the pressure of our leg or whip. So, if we want our pony to move laterally (i.e. to the side) we will flick our pony with the whip on the side we want him to move away from. It is important to apply the whip to pony's side, not back. Thus, to have the pony move to the left, flick your pony's right, near the bottom of the ribcage, side with your whip.
As an aside: we want our pony to yield to pressure when applying either leg aids or rein aids. When we apply pressure on the reins, we are asking our pony to yield to that pressure whether it be by slowing down (if pressure is applied on both reins), or turning (if the pressure is applied on one rein). Indeed, even when we apply a slight amount of rein pressure to achieve suppleness, we are still asking the pony to yield to that pressure by carrying his head and neck in a certain manner (if rein pressure is applied correctly, proper head carriage decreases the rein pressure felt by the pony). This works because it is natural for a pony (either human or bio) to move away from pressure.
Once your pony understands and obeys leg/crop aids (the basics of which should be instinctual - it is natural for him to move away from pressure and the crop), you may want to teach him the four basic gaits used in pony play.