In his Shotgunner's Notebook the late author, Gene Hill, said, "...in my opinion the perfect shotgun is one that I'm entirely unconscious of; it is merely a place to put two shells. I don't see barrels, I don't feel stock--it's part of me, like pointing a finger or, simpler, just looking. And that's the secret here: just looking. As simple as it seems, a vast number of gunners sight down the barrel instead of looking at the bird. Let me assure you, you can't do both and be a good wingshot. You must ignore the gun and look, and look hard, at the target--and wherever your eyes go, the gun barrel will go all by itself! Doesn't that sound easy? It is and it works."
This is sage advice, and it fit me to a "T". For the first year or so that I shot a shotgun I was guilty of the sin of "aiming" rather than pointing. My initial exposure to shooting was via the NRA, using a .22 rifle, so this came quite naturally. It took a week at the Remington Shooting School to cure me of this when it came to shotgunning, but it did the trick because (as Gene counseled) they taught me to look at the target. Also, I found that I was shooting under most of my trap and skeet targets because I was stopping the gun (another complication of aiming) while they continued to rise.
Cntryboy 1289 was right when he recommended following-through. By maintaining your swing even after you see the target break (or not), you will avoid stopping the gun.
I hope this helps.
Good luck, and good shooting!
