Make a homemade soft benchrest of some kind to stabilize your pistol. I made a simple one out of a small duffle bag stuffed with towels. There is no way you can be absolutely sure where your piece is aiming when the human factor is so influential as with offhand shooting.
Then, buy a stack of economy paper plates at the grocer. Draw a dime size black spot in the center for your aiming point and stick 'em up on your backboard. Pace off 10 yds and go to work. You will find this exercise is VERY enjoyable and informative.
Also, .22's are very particular about ammo. You'll go nuts chasing the holes around trying to adjust your sights when switching brands around. Some will shoot left, some will shoot right, some high, some low.
A bench rest will allow you to determine which brand your gun likes. This is a really fun way to enjoy your .22. I know what my Buckmark shoots best, but every now and then I find something on sale at a gun show or a store, so I get out my plates and duffle bag and see what it really does.