Nutshell-wise, here's the skinny...
My position is that it's difficult to become a good field shot or beer can shot without first becoming a good shot on paper bullseyes.
First thing is to start out with a shooting iron which is known to be fairly accurate. This means a .22 rifle. This means, next, a rifle with clean Patridge sights, flat rear sight with a square notch, front sight a square post, and just a little daylight between the post and the notch. Use sight blacking.
This also means a crisp trigger letoff.
This means using decent ammunition. (For some reason, and I know I'll get flack for this, Federal always seems to work best for me regardless of caliber.) Use standard velocity ammunition.
This means starting out with a good rest --sandbags and a solid bench and solid seating arrangements. Not so important with a .22 rifle, with so little recoil, but you must hold the rifle exactly the same with both hands, and it must rest on the sanbags the same for each shot. If it's an autoloader, so much the better.
The object of this is to develop your sense of a sight picture. I disagree that a smaller target is easier to sight at. Use a pistol 50-yard repair center target at 25 yards with an 8 inch bull. I use it for rifles at 100 yards.
Do not walk your shots around the target to hit the center. Just fire each shot independently using the same sight picture. The object here is to prove your sight picture is adequate, not that you can hit the X in the middle.
After you've established a reasonably consistent group you can move your sights (rear sight in same direction as the direction you want to move the group --rear sight up to move the group up, rear sight left to move the group left, etc.) Do not try to move the sights between shots. Take a group first.
They say to focus your vision on the front sight, leaving the great big fuzzy blob of the target sitting over the post, and with the rear sight only slightly out of focus.
Make sure this big fuzzy blob is sitting over the front sight. Don't try to "center" it on the front sight. If you try to sight on the center, your eyeball does not know where it is except for being somewhere in the black. If you have the big fuzzy blob sitting completely over (but just touching) the front sight, you then know where you are in relation to the aforementioned big fuzzy blob.
When you're sighting, "scan" a couple of dimensions in "quarters." That is, is the big blurry blob centered over the front sight? Are the small bars of light between the front sight and the rear sight the same? Is the big fuzzy blob still over the front sight while you're sqeezxing the trigger? Is the top of the front sight still level with the top of the rear sight? This scanning goes on constantly while you are increasing the force on the trigger.
To make the miniscule little changes to adjust your sight picture, don't move your whole body. Just increase the force with the heel of your hand on the grip or the forend, for example a teeny bit and the wights will move accordingly.
After a while, you'll be able to "call" your shots. That is, you'll know whether the shot was off or not. A marksman will get to the point where he/she can predict just about exactly where on the target he/she would hit with each bad shot: "Damn. Seven ring at 1 o'clock." (This is called a "called flyer.")
They say if you can "call" your shots, you're a marksman, and this can be done only if you've developed a sense of the proper sight picture.
Breath control: This varies with the shooter. I take only one deep breath once I'm in position, two more little puffs, then another full breath and let some out before I hold it. Do not hold your breath until you feel you "need" to take another breath. If it's taking that long to establish the right sight picture, stop squeezing the trigger, do the deep breath, little breaths, full, and hold again, and continue the trigger force increase. I find the full breath increases my body rigidity because of the internal pressure. Others recommend differently.
Don't hurry the process because you're running out of air. It's been a long time, but I believe you are allowed three minutes between shots in the slow fire high-powered stages of a match, so even the best shots may repeat the process several times before the shot is actually let off.
Trigger control: There is a bit of confusion over this. For beginning shooters, it is usually best to squeeze the trigger gradually until the shot is let off as a surprise. However, with a good light target trigger, you should know when the gun will go bang and you time this "bang" with when the sights are just about to cross the target where you want the bullet to hit. This is kind of advanced, but this need to "know" when the trigger will let off is the reason for the popularity of set triggers in so many unlimited matches. These things will let off at only a few ounces, thereby allowing the marksman to "time" the exact instant of firing with just before the sights align exactly on the target.
All this is called "trigger discipline," and I'm sorry to say it takes practice before the individual skills all blend into an automatic procedure that just "happens" with each shot.
After you get done bench-rest shooting and establishing this automatic process (and getting your rifle sighted in), you can graduate to shooting "freehand," as it were, that is, off the bench. If you are taking shots with a rifle, you should use the sling, even if it's just a "hasty sling" configuration. Having that sling swinging around while you're trying to shoot is not conducive to accuracy.
This is not to say that you can't have fun shooting handguns all the while you're developing your riflery skills. In fact, you will find a considerable tranfer of learning from the rifle to the handgun. But using a rifle at first, with its inherently more accurate long sighting radius, will allow you the feedback on your grouping without introducing the variable of the short sighting radius of the handgun.
Then, and only then, can you graduate to beer cans at 100 yards. Nothing to it. Just imagine the beer can in the center of the aforementioned big fuzzy black blob.
Well, gotta go to the range and practice my groin shot. Nothing to it. You just imagine the groin in the center of a big fuzzy black blob.