One of the key aspects that attracted me to practical pistol competition was the shooting while moving. A static range can be fun, but shooting while moving through a course of fire and moving from one position to another is even better. Learning the right techniques will get you on target faster with the best possible score.
When exactly should a target be engaged on the move? This largely depends on individual skill level. In general, I like to shoot on the move at ranges inside the 12-yard mark if the targets are big enough. If I am really feeling it that day, I may stretch that distance to 15 yards. Since foot speed will slow when shooting, the biggest decision to make is if the distance covered while shooting mobile, combined with the inherent risk of dropping points outside the A-zone is better than guaranteeing perfect hits from a stable platform and moving at a faster, uninterrupted pace to the next position. From my experience, when dealing with targets at distances greater than 12 yards it is usually better to settle, shoot from a static position and then move aggressively to the next position.
After deciding it is time to be moving and shooting the goal is to get the sights aligned and squeeze off accurate shots while covering a lot of ground. The single most important item to remember when shooting on the move is to bend deeply at the knee. Just as bending the elbows helps stabilize the pistol and absorb recoil, bending at the knee translates to (1) greater acceleration and deceleration, (2) ability to cover more ground per stride and (3) stabilizing the sights with the least amount of disruption.