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The most difficult part of shooting any gun accurately is trigger control. Here is my step by step guide to proper trigger control. A lot of this material came from taking Louis Awerbuck classes, especially the follow through and trigger reset sections. Follow through and reset are the most underrated areas of trigger control, and learning them helped me a lot. Any part that you think is incorrect is probably from my interpretation of the material.
During this whole procedure, you should have a hard focus on the front sight. This is because you're trying to line up the rear sight, front sight, and target. By focusing on the middle object, you can best keep all three aligned.
1) Touch the trigger.
What part of your finger you use depends on both the gun that you're using, and your own body. You should pull the trigger somewhere between the tip of your trigger finger and your first knuckle. It doesn't need to be complicated, because you'll instinctively know what's right. But here is an analysis for those who like to think about things in detail. The part of the trigger finger that you use depends on:
a) The weight of the trigger pull and your own hand strength. Pulling the trigger with the part of your finger near the tip may have finer control, but it will be weaker. Pulling the trigger with your first knuckle will have a little less fine control, but have more strength. You'll want to match the strength of your pull with the weight of the trigger.
b) The distance between the trigger and the back of the grip, and the size of your hands. A long trigger like on a double action revolver may require you to touch the trigger with your finger closer to the tip, especially if you have small hands, which would be undesirable since the trigger pull would be heavy. (see http://www.personaldefensenetwork.com/articles/handguns/dealing-with-the-double-action-trigger/ for more on double action triggers). A gun with a short trigger and thin grip like on a 1911 would allow you to use any part of your finger that you choose.
2) Take up the slack
Press the trigger through the light section of the pull until you start to feel some resistance. If you just smash through the slack, then when you hit the firm part of the trigger, you'll have too much momentum and slap the trigger, pulling the gun off target. Thus this section has to be distinct from step 3.
3) Press the trigger directly to the rear until the gun goes bang
As you press the trigger it should be moving at a constant velocity. We don't want any stop and go. During this process, the sights will be wobbling a little on the target. Accept this, and don't try to hit perfectly. If you try to wait until the sights are perfectly aligned and then yank the trigger fast, you will pull the gun way off target.
4) Follow through
After the gun goes bang, the muzzle will rise a little. Maintain focus on the front sight. Do NOT look at the target to see where you hit. If you get in the habit of looking at the target immediately after shooting, you will sometimes lower the gun while shooting so you can see the target, and end up shooting low. After you pull the trigger, the sear releases, the striker/firing pin hits the primer, which ignites the powder, which creates expanding gases, propelling the bullet out the barrel. This all happens pretty fast, but you can mess it up before the bullet leaves the barrel.
5) Reset the trigger
Keeping your finger on the trigger, let the trigger out just until you hear and/or feel a click, indicating that the trigger has reset and the gun is ready to fire again. Do NOT chuck your finger off the trigger immediately after shooting. If you get in the habit of taking your finger off the trigger immediately, you will sometimes end up shooting left(as a right hander). For that reason, you should always reset the trigger before taking your finger off the trigger, even if you're only taking one shot.
However, if you're taking more than one shot, there is an additional benefit. When you only let the trigger out to reset, the next trigger pull will be as short and light as possible for that particular gun, which means you start about halfway through step 3 for your next shot.