Breathing can be important. The inhale exhale motion of your chest can cause the barrel of the gun to wander. It's important to try and keep your breathing steady and even as you are shooting.
Another thing to keep in mind is to try and track the target. You're not trying to aim so much as point ahead of the clay pigeon (I'm assuming we are talking about clay pigeons and not just stationary targets). It's going to take a few tries to get the feel of it, but you will want to become familiar with the arc of the pigeon across your view. You're going to try and have your gun swing to slightly in front of the path of the pigeon before you pull the trigger. Exactly how far will depend on how far away you are from the pigeon's path.
Beyond that, I'm pretty new to it too, so I'm still figure it out. Good luck!