Sighting in a scoped rifle is a simple process, let me tell you how I do it. The scope I'm sighting in was mounted back at the shop, the base and ring screws were properly torqued, and the crosshairs leveled. I also set the scope as far forward as possible for maximum eye relief.
The first step is to boresight the gun the old-fashioned way, starting at 25 yards. With the bolt out, I look down the bore and center the bullseye. Then, without moving the rifle, I adjust the crosshairs to the center of the target and fire one shot.
Here's the next step; with the gun still in the rest and the crosshairs on the bullseye, I turn the turrets as necessary to move the crosshairs to the bullet hole I just made. The gun must not move from its position as I make these adjustments.
I shoot again to verify that the rifle is nearly sighted in at 25 yards and make any minor adjustments. Now a fresh target is set up at a hundred yards with the crosshair centered on the bullseye. I fire another shot--looks pretty good. I adjust the elevation to bring the point of impact two inches above the center of the target then adjust the windage to the center.
Now I can feel comfortable shooting out to about 300 yards, then I'll fire a few test groups. For guns like a Ruger 10/22 that you can't see through the barrel from the back, a bore sighter can be used. The process for sighting in the gun is the same. I get it on paper at 25 yards, but since this is a rimfire I move the target back to only 50 yards.
After the first shot, I can make any needed adjustments then shoot for a group. I want this rifle dead-on at 50 yards so the group is centered in the bullseye.