Long Distance shooting
From the title, I thought you meant long distance, 200 yards and up....
The essentials for hitting at long range are the same as hitting at any range where you use the sights. You simply line up the sights correctly for the range, aligned on the target, and squeeze the trigger.
The handgun need to be up to the task as well. Nearly all are, its the shooters who are not. Many revolvers have one chamber that does not shoot exactly where the rest of them do. Seldom an issue, unless you are talking bullseye accuracy or long range shooting. The round that's a couple inches outside the rest of the group at 25yds can be off a couple feet or more at 200yds. Learning your gun and load will teach you which misses are your fault, and which are the gun's (if any).
Many autoloaders will print the first round a little off from the rest. Different reason, but the same result.
To learn to shoot at long range, a couple of things are very helpful. First, you need a backstop that shows you where your bullet hits. Second, you have to be able to see it. A spotter can be helpful. Once you learn where your bullet hits, with a given sight picture at a certain range, it is a fairly simple matter to change your sight picture to get the bullet to hit your point of aim.
Of course, you also have to be consistant. That's where most people have difficulty at first. I'm talking offhand, unsupported shooting here, just to be clear. The little wobbles and bobbles that don't matter at 15 feet DO matter at 200yds.
A good trigger pull helps a lot. You can be long range accurate with a fair or even a poor trigger pull, but you, the shooter, have to work harder.
Forget speed. Speed is for close range, defensive type situations. This is what most people practice, for the good reason that its the most likely thing they will need, and if they do need it, they will need it badly. Long range shooting is recreation (with a remotely possible practical use). Be relaxed. Don't rush.
Take a coin, and place it on top of your EMPTY gun. Aim and dryfire. The coin should sit there until the gun "fires" (hammer falls) Practice until you can do this. Once you can do this, regularly,
balance the coin on your gun. Lots of guns have a small flat spot where you can do this (I try to do it on the front sight). Same process, practicing a steady hold. I can balance a dime on the front sight of my Ruger Blackhawk, and when I do my part right, it stays there until the hammer falls.
Once you can manage a good steady hold, we'll talk about what sight alignment will get you hits at long range.
I can, and often have rung the 200yd gong at my local range. Given a reasonably calm day, I'll do it with any handgun you give me, before its empty (ok, not with a single shot, but any repeater...
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.22s are tough, you virtually need a spotter (with some optics) to spot the misses, but as long as you can tell where the bullets hit, you can adjust to get hits where you want, with anything. My technique works with any caliber, any barrel length, any gun. Some guns have a much steeper learning curve than others, but it can be done.
You mentioned being nearsighted, that is a complication. For long range hits, you have to be able to see your target, and you front sight, well enough so you can consistently put the front sight where you want it, in relationship to the target. It does take more precision than aiming COM at 7yds. If you can see you long range target as a fuzzy object on top of your front sight, we can work with that. IF you can't, go see the eye doc or find a different hobby.
