Practice makes perfect. This saying holds very true concerning our ability to make a good, lethal shot on an animal with a rifle. Our hunting ethics dictate we respect the animal enough to know our limits and capabilities when considering a shot.
There is no substitute to trigger time. This can be as easy as dry firing your rifle at home. This allows you to practice your body positioning, the trigger pull, breathing, and follow through. Live rounds are even better, so spending time at your local range is imperative. At the range, make sure to practice shooting from all positions, not just from the rest on the bench.
Bench shooting is great for properly zeroing your rifle, but it has little resemblance to real world small game hunting situations. To practice for the real thing, you want to work on prone, seated, kneeling, and standing shots without the use of a rest. But the really important thing is to learn to shoot well with improvised rests such as walking sticks, tree limbs, fence posts, and downed logs. I have killed many, many squirrels and rabbits with a .22 and I’d bet that I used an improvised rest on over 90% of the shots I’ve taken.
When shooting, your focus must be on the shot alone. I like to run through a brief checklist in my mind just before taking the shot.