Having addressed the subject of airgun power, we should now consider the issue of preparing for the hunt. The question is not so much of power, but how effectively can that power be delivered to the target keeping in mind that the area of the target that must be hit may be only about an inch in diameter. An air rifle may be capable of shooting one inch groups at 40-50 yards from sandbags on a concrete bench, but if the shooter can hit a target of that size only at 20 yards under field conditions the shots at game must be limited to the skill of the hunter.
Under field conditions, shots at game may have to be taken with offhand shots from a standing position. Practice shooting in that postion. Because the game animals are not black circles, obtain or make life size cutout targets of animals and practice on those targets. It can be rather distracting to try to get a good sight picture on an animal if all of your practice has been at black or orange bullseyes at known ranges. If possible, practice by placing the targets in realistic positions at random distances and see how effective you can be at placing the pellets exactly in the lethal zone on the target.
Often in hunting, a convenient tree, post, or stump can provide a rest from which to shoot. Practice shooting in these situations so when the moment arises you are able to quickly assume the best possible position from which to take the shot at the game. Know your limitations and adhere strictly to them with regard to how long a shot to attempt. Do not let a scope with a range finding or Mil-Dot reticule tempt you into taking a shot that is beyond your skill as a shooter. As described earlier, a properly sighted in air rifle shoots so that the path of the pellet crosses the line of sight at two distances. Know the trajectory of your rifle/pellet combination well enough to know what those distances are. Do not sight in your air rifle at such a long distance that the pellet path is ever more than about an inch above the line of sight. If you do, it is easy to miss small targets at intermediate distances.
There is frequently a great deal of difference between the flight characteristics and accuracy given by different types of pellets so practice shooting with the same type of pellets you will use when hunting. It is important that the hunting rifle be sighted in very carefully with that type of pellet. Your air rifle may give outstanding groups at 10 meters with some light wadcutter pellet, but if you are going to hunt with a heaver pointed or hollow point type it is essential that you know exactly how your rifle shoots them.
Practice will make you a better shooter under field conditions, but in order to be a true hunter in the ethical sense you must apply the factors of judgment. If you are not sure that the pellet can be placed where it should be, do not shoot at an animal. When using an air rifle, you do not have much of a margin of error.