I clean my 22s by using an old nylon toothbrush and a little Hoppes #9 on the bolt face and breech face. Then I squirt a little Hoppes into the chamber with an eye dropper and let it sit a few minutes.
After those few minutes, I run a Bore Snake from the chamber thru to the end of the barrel a few times. HOWEVER, when I bought the new Bore Snakes I used a sharp razor blade to cut out the wire brush (and then took it to a shoe repair shop to be resewn) so as not to dammage the chamber and/or barrel.
At least once a season, or every 1000 rounds (approx.) I remove the bolt from the rifles and clean the firing pin, extractor, etc. but do not change the Bore Snake routine but I do scrub the chamber a few times with a brush.
For .22 handguns, the procedure is the same but I take out the bolts a bit more frequently than the rifles.