Two ways to do it: First, "sustained lead", where you actually swing with the bird at its pace (slightly ahead of it) and pull the trigger when you fell comfortable that you've indeed matched the bird's speed; or, "pass through lead" (which I prefer) where you actually swing faster than the bird and pull the trigger when you see an appropriate amount of open space between your barrels and the front of the target. I like this better because I feel I can get off the shot a little quicker, but it takes more practice than the sustained method. Either way, it is imperative that you follow through with the swing after having pulled the trigger.

Good Dogwork and Good Hunting