Practice makes perfect. This saying is very true regarding our ability to make a good killing shot at an animal with a rifle. Our hunting ethic dictates that we respect the animal enough to know our limits and capabilities when considering a shot.
There is no substitute for turning on time. This can be as easy as dry firing your rifle at home. This allows you to practice your body position, trigger, breathing, and tracking. Live rounds are even better, so spending time at your local range is imperative. On the shooting range, be sure to practice shooting from all positions, not just from the rest of the bench.
Bench shooting is great for properly zeroing your rifle, but it bears little resemblance to real-world small game hunting situations. To really practice, you should work on prone, sitting, kneeling, and standing shots without the use of a break. But what’s really important is learning how to shoot well off makeshift breaks like canes, tree branches, fence posts, and fallen logs. I have killed many, many squirrels and rabbits with a .22 and I bet I used an impromptu rest on over 90% of the shots I took.
When shooting, your focus should be on the shot alone. I like to go through a short checklist in my mind right before I take the shot.