Fundamentals of Markmanship
Air rifles can be either powered by Carbon Dioxide (CO 2) cartridges, or with an internal pneumatic pump, either with multiple pumps for increasing power or a single pump (as with “break-barrel” models of rifles). For the most part your standard air guns come in either .177 or .22 caliber models. Beeman  offers one that has interchangeable barrels in both calibers, with the velocity decreasing slightly as the caliber is larger.
There are many things you can do with an air rifle from a hunting  and survival perspective. You can hunt small game quietly without the need for a suppressor if you’re doing it on the q-t, and ammo for it is both affordable and (when the SHTF) able to be reproduced simply (refer to the recent article I wrote on how to build your own forge).
The air rifle or air pistol fires pellets and/or BB’s (little ball bearings) that can be reused repeatedly. There are several “trap” targets like this one  available with replaceable buffer materials on the inside. These targets enable you to collect your air rifle ammo and use it again. It is a simple thing to set up a range within your own basement or out in your backyard with an air rifle or air pistol. Although the motion of the weapon in terms of recoil is reduced from that of a rifle, the fundamentals of marksmanship are the same. Here they are:
Breathing: Before you pull that trigger, you need to control your breathing, and optimally should pull immediately after you have exhaled
Aim: Self-explanatory, but it involves you zeroing on your target to line up your sights with your eyes and enable you to hit that bullseye.
Trigger squeeze: Should be accomplished with the very tip/end of your index finger, and should be a smooth, non-jerky action akin to squeezing a lemon
This article is not intended to cover rifle marksmanship in general; however, you get the picture. Hand-eye coordination and the employment of these three fundamentals can be accomplished effectively with the air rifle. There are several European and Korean firms that manufacture air rifles in “big bore” calibers that can take down large game, if you wish to pursue air rifle marksmanship further. For starters, you can take your pick from Daisy, Crossman, Beeman, Benjamin, even Ruger, among others in the two mentioned calibers.
Just remember to lay out your range in a professional and safe manner. Treat your air rifle as a firearm at all times, as it is a type of firearm that can hurt someone severely, or worse if misused or used in an unsafe manner. As a field-expedient trap, you can even make one out of telephone books/directories mounted in the front of a carboard box. These work better for BB’s, as the pellets are usually made of lead and the strike tends to deform them. Safety glasses  or goggles are also recommended, as a ricochet can come straight back in your direction.
The air rifle or air pistol are great tools to introduce your kids to principles of firearms safety and train them in marksmanship. It is quality time spent with them, in which they will learn how to do things the right way before they are old enough to fire that .22 rifle or that Winnie ’94  for the first time. Affordable and effective, the air rifle is an excellent training tool that you never really outgrow, and can enable you to have your own indoor range during the winter months that is both safe and cost-effective. Be safe, take care of one another, and happy shooting!