Look at the bird, not the barrel. A shotgun is pointed like a finger, not aimed like a rifle. If you are consciously seeing the front bead, your eyes are in the wrong place and you will miss behind.
Mount the gun to your face, then bring both to the bird together. A gun mounted to the shoulder first, then muscled up to the cheek, arrives late and crooked. Practice the mount at home in a mirror hundreds of times — it costs nothing and fixes more misses than any lesson.
Use swing-through: start the barrel behind the bird, accelerate through it, and fire as the muzzle passes the beak, then keep swinging. The follow-through is not a formality; stopping the gun at the shot is the single most common cause of missing behind.
For crossing shots at 30 yards, a duck at 40 mph needs roughly four to six feet of lead — far more than instinct suggests. On incoming birds, blot the bird out with the barrel and fire. On going-away birds, cover the bird and shoot right at it.