I am an expert, and this is pretty much correct so I will quote you :P. Most .22 ammo is indeed rimfire, meaning the primer is contained in the rim of the casing. To fire it, the rim is crushed, which ignites the primer ring. Other rounds (such as 9mm) are centerfire, meaning there is an easily removable primer in the center of the case.
You can reload .22 without any particularly special equipment except for a properly sized crimper and appropriate bullets* (mix “strike anywhere” matchheads with water to create a thick liquid, then dip a q-tip it in and use that to squish it into the bottom of the case. There’s fancier ways to do this, but this does work fairly well and requires less for tools than other ways), but there’s no good way to do it, and because each firing crushes the rim, you only get a reload or two out of it before ignition becomes too unreliable to be worth it.
*Which need to be cast, really. .224 diameters don’t work because .22 is a heeled bullet.
