How does it work? Like crap in my opinion, I bought one for my single shot H&R rifle and mine works pretty simply, but accuracy is less than stellar. My chamber adapter looks just like a .223 case made of steel, and has a plug for the back that has a rimfire firing pin milled onto it. You drop the .22 rimfire cartridge in the adaptor, put the plug in, close the action, and when the firing pin strikes the plug it has enough force to ignite the rimfire primer.
Here is where I realized it's a waste of time to use a rimfire adapter. I had to extract the chamber adapter every time to use a dowel, section of cleaning rod, ice pick, or small screw driver to push the fired cartridge out of the adapter. Plus my accuracy was never better than about 6" at 25 yards with any .22 LR I tried in my rifle.
The accuracy problem comes from the fact I don't think that .22 LR has the power to obturate (deform) the base of the bullet to make good contact with the rifling. A .22 centerfire rifle uses a bore diameter of .224 and a .22 LR uses a bore of .223 or slightly smaller. While .001 doesn't seem like a whole lot, there isn't a whole lot of force behind those bullets to push the base out to contact the rifling.