Shotgun sports are by far the most intriguing of all gun sports. Using a shotgun properly is an art form and, like tennis or baseball, using a shotgun is a pure hand/eye thing and the analogies are all with baseball or tennis, there is no analogy to any other shooting sport. Like tennis or baseball, you watch the target 100 percent; if you ever watch any part of a shotgun, you'll never hit anything with it. That sound simple, but is VERY hard to get used to if you're used to any other sort of weapon. Particularly in the case of skeets in which you track targets over a considerable distance, the use of legs and hips is entirely similar to that in baseball or tennis.
There are several kinds of shotgun games, skeet and trap being the two most basic. The best starting point for trying to figure this stuff out aside from basic lessons is going to be
www.sunriseproductions.us, particularly Todd Bender's skeet DVD. Some of those tutorial DVDs are a bit pricey, going for around $55, but that one in particular is a basic ticket of admission.
I share Bender's opinion that you have to shoot with a constant lead to have any chance in actual skeet competition. For purposes of hunting with a shotgun you need to be able to swing through and/or pull off of targets as well, in other words a hunter has to have some prowess at all three basic methods of shooting moving targets.