Shooting clay pigeons, whether for fun, as target practice for hunting, or as part of a competition, can be a rewarding experience. It takes years to build proficiency, but with the right stance, aim and shot, you'll be nailing clays left and right in no time.
Stance and Preparation
To aim well you must have balance and mobility, and these come from a proper stance. Stand with your feet shoulder-width apart, with your left foot forward downrange and your right food back (reverse if you're left-handed). Hold the butt of the firearm firmly against your shoulder. Before competitions, practice bringing your firearm from a neutral position into a firing position quickly and repeatedly to stamp this motion into your muscle memory, making it much easier to pull off once the pigeon is in the air.
If you are practicing for a hunt, start from a position you will likely be walking in as you hunt and practice bringing your firearm around to aim. Adopt a neutral stance and shift into a firing stance once the pigeon is released.
Familiarise yourself with your weapon's aiming mechanism before coming to the range. Practice lining up the sights quickly and repeatedly to stamp this into your muscle memory like you did with the firing stance. When the pigeon is launched, you must achieve a good line on your sights, even before aiming. Once you know you will shoot straight when you pull the trigger, lock your arms and shoulders and rotate from your waist to aim. This may seem strange at first, but it is imperative that you maintain a straight line with your sights. This is a lot to account for once the pigeon is in the air, especially if you are starting from a neutral stance, so practice often.
If possible, find a large mound of dirt or ridge you can fire a few rounds at. Don't fire at anything in particular, just shoot at the side and watch how long it takes for the pellet spread to make contact--it is quite a bit longer than most people think. Just seeing this with your own eyes will help you know how much to lead a pigeon while it is in the air. How much to lead a pigeon depends on its speed and the distance it is from you once you get a bead on it, so take both into consideration. Imagine a line coming out the end of your barrel, and when this line hits the appropriate lead point, firmly squeeze the trigger.