I encountered a couple people this weekend who had never shot a shotgun before and had no idea how to do it properly. Here is a little primer. If you're right handed this should make sense for you. If you are left handed then reverse everything. You backwards brained folks should be used to doing that.
Lets start with the feet and work up. You should have a basic idea which way you need to be facing. Great, now put your left foot forward pointed in that direction. Your right foot should be back about shoulder's length away from it. You should have good stability using this stance, if you don't you may need to adjust the position of your feet a little.
Pick up the gun and put it to your shoulder. MAKE SURE IT ISN'T LOADED. I'll tell you more on the "mount" in a bit, right now you just need the weight of the gun to get your balance right. At this point some people will have a tendency to put the gun out front and lean back onto their right foot to balance the gun's weight. Don't. You want to put most of your weight on your forward left foot and lean towards where you are shooting. When you fire the gun it will push you back onto your right foot. This way you can use the big muscles in your legs to help absorb recoil instead of using your weaker upper body muscles. You can also ride the recoil a bit with your upper body and that will make it hurt less.
Ok? Now lets move up. Your waist is for twisting left and right to track your target (since most shotgun games involving moving targets).
Now lift your right arm up so it is parallel to the ground. If you feel your shoulder, you will notice a little divit between your chest muscles and your shoulder muscles. That is the pocket or cup. That is where the butt of the shotgun goes. Lift the butt of the gun up to your shoulder and put it there. Your right arm is out because this will keep the pocket nice and deep. As you get better you can lower that arm, but trust me you want it out to start with. If you lower your arm now, the gun will probably jump out of the pocket under recoil and beat its way down your arm. That will hurt like heck so keep your arm up for Christ sakes.
Now pick up the shotgun. MAKE SURE IT ISN'T LOADED. Your right hand goes on the stock by the trigger. Your left goes on the forestock under the barrel(s). Put the butt in the cup so you get as much contact as possible between the butt of the gun and your shoulder. This will spread the impact out and it will hurt less. Hopefully the butt pad on the gun is a good shape to fit the contours of your shoulder.
Now let me say a few things about shotgun fit. Its a personal thing and a lot of what you are going to read next will vary with fit. Chances are you aren't using your own gun if you are reading this, so you basically have to take what you can get. If you buy your own gun you want a stock that is the right angle/length/shape for you. If your gun doesn't fit you will have a much tougher time with it. Recoil will hurt more and accuracy will suffer. Keep reading and I will bring up fit a bit more. Keep in mind if you want a really good fit, most hunting shops have professionals that do that sort of thing.
Now your right arm holds the gun into the pocket. Your left arm pulls the gun back into the pocket more and also controls how you swing the gun. On a pump shotgun pulling back on the forearm will also have the advantage of helping you pump faster after each shot. How hard should you be holding/pulling? A wise man once said you should be holding the shotgun like a injured bird, you don't want to hurt it but you don't want it to get away either. That sounds good to me.
Now if the stock is the right length and angle (called pull and drop in the gun world), your right cheek will be against the stock and you will be looking down the barrel of the gun. Most shotguns have bead sights, so there is probably a little aiming bead at the end of the barrel. If the stock is too long/tall/etc you will be looking at the back of the gun. Conversely if the stock is too short you will be looking down the barrel from too high up. If it fits you shouldn't really see the top of the shotgun or the barrels at all, only the sights where they stick up. Raise or lower your head to try to get the right sight picture.
If you can't get this sight picture no matter how hard you try, find a different gun. Production stocks are a little long for most people, although they fit me fine because I'm a little taller than average. In general its better for a stock to be too short than too long. Kids and women might be better off with a youth (also called "bantam") stock.
Now, as I said before, your cheek needs to be against the stock. Some people try to avoid this because they think it might hurt. It shouldn't even if the fit isn't the greatest. This cheek position is called the cheek weld. With bead sights your eyeball is the rear sight, the cheek weld locks your eye into position with the gun. If the stock "fits" then your eyeball should naturally be in the right place. If not you will have to move your head and chances are that it will be easier to lose to proper sight picture. Sorry people shooting loaners.
Now point and shoot. Many a shotgunner has told me that you don't aim a shotgun, you point it. You are firing a cloud of shot remember. With a pump make sure you pull the fore-end all the way back and push it all the way forward for best reliability. Leading a target is something you have to get a feel for with experiece but hopefully you will be starting on easy, slow, close targets. Enjoy shotgunning, it can be very satisfying once you start popping clays.
That's about it. I taught somebody these basics during my shooting expedition this weekend and he went on a hot streak and almost beat me. I wish he could have returned the favor and taught me some stuff. ;)