Buy yourself a well known to be accurate "bolt action" rifle that doesn't cost a lot to shoot. A .22 will be the best by far. Get something better than a 10_22, which is semi-auto anyway and that is something that will prevent you from using this method. There are lots of better choices for learning accuracy. Buy yourself a cheap laser that can be mounted on your rifle. This is key.
I would suggest something like a Savage MkII or a Marlin XT. Both are drilled and tapped to mount scopes which means you can mount your laser. You won't even need ammo at first. You will need just one empty shell casing. Having several is probably a good idea. Once you mount your laser you will want to leave the empty casing in the rifle. Be absolutely certain you don't leave a live round in the gun. Check it each time you start to practice.
You don't need to even zero the laser. That won't be the point. What you will want to do is to hold the rifle in a way that is natural for you to hold it. Try to hold it like you would hold a rifle that has a scope. If you don't know how that works borrow one or just pick one up in a gun shop just to look at it. You don't need to buy it. You just need to have an idea how to hold the rifle.
Be sure to hold the rifle the same way every time. I'm talking keeping everything in the correct position. At first this isn't as important but it will help you down the road if you read a web page or two about how to correctly hold a rifle.
What you want to do is to practice pulling the trigger. Turn the laser on and put the dot on something maybe 15-20 feet away. You can do it inside if you like. Keep that empty case in the chamber because rimfires aren't meant to be fired without a round in the chamber. A spent round will do. It keeps the firing pin from hitting the side of the chamber which will prevent damage to your rifle.
The idea is to learn to pull the trigger so that the dot doesn't move off of your target. This is the main point of all this. You will never be a good shot until you master the trigger pull. It is by far the most important aspect of shooting. If you move the gun around when you pull the trigger you will certainly be missing what you're aiming at. You absolutely must have a solid trigger pull where the rifle doesn't move from where you're aiming as you pull that trigger.
The absence of the bang of a bullet being fired or the flash of the muzzle will make sure you aren't startled into missing too. Anything that makes you move that laser dot off the target when you pull the trigger will make you miss.
Practice pulling the trigger until you can do it in your sleep without messing up. Learn how to control your breathing so that doesn't create problems. Learn to keep from pulling the gun one way or pushing it another way or moving it up or down.
If you learn to keep that dot on your target then you have more than half of the battle won. You will already be a good shot if you can do that. You just have to learn how to aim and learn to not let the bang of the bullet cause you to move the gun. You might even try using the laser while shooting a round so you can see you aren't moving the gun while firing a live round.
These other things are important too but they are easier to master than the trigger pull. Get your stance down and the way you hold the gun down and learn how to aim and you're there. Shooting is really a simple thing to do. It just takes practice but you have to practice doing the right things instead of the wrong things. And keeping that trigger pull under control is the most important part of shooting. I'd say it's at least 80% of shooting accurate.
I think you'll be amazed at how well you shoot if you do this. Nothing else will get you to being good faster. I'm not the best shot on earth but I'm pretty good. I've won a bunch of contests. And these are things I still practice sometimes especially if I haven't been shooting for a while (like after a long winter - where's my laser?
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