Here's how I sight in:
Plop the rifle onto a bench rest. Put up a target at 25 yards. Look down the bore of the rifle, and make sure it is on the bullseye. Adjust the scope so it is also on the bullseye. (This is right for most bolt action rifles. If your scope is far above your bore, as in an AR15, it won't be. With my AR15, the bullet is 2" below the crosshairs at 25, 1" below at 50, and right on at 75.)
Aiming at the bullseye, fire one shot. Without moving the rifle, adjust the crosshairs so that they cover the point of impact.
Move the target to 100 yards. Fire five shots. Find the center of the group. Without moving the rifle, adjust the crosshairs so that they are 1 1/2 to 2" below the center of the group (assuming you're shooting 2700 FPS or faster rounds). How far below depends on how much above the line of sight your bullet should be at 100 yards, according to where you want your second crossing to be (usually 200 yards).
Your rifle is now sighted in. Usually, I follow this up with multiple groups, just because it's fun.
Here's how I mount the scope:
First get a tube of blue Loctite, #242, and a torque screwdriver such as the FAT screwdriver offered by several suppliers.
The front base screw is often troublesome. Temporarily put the scope base in place, and put the front screw in the hole. Turn it backward until you hear a clunk that indicates that the male and female threads are in position to just barely start to engage. Now turn the screw forward until it is firmly seated, counting the turns as you go.
Then remove the base, and repeat the procedure. If the number of turns with and without the base are equal, the screw is bottoming out on the back end of the barrel, and not holding the base in place. Grind a bit off the end of the screw so that the screw firmly holds the base, rather than bottoming out.
Now put a drop of Loctite on each base screw, and torque it in to 30 oz inches.
Put the scope in the bottom half of the rings. Put the front top ring in place, and gently tighten it. If the scope comes up off the rear ring, your rings are not aligned. Then remove the front top ring, put the rear ring in place, and gently tighten to see of the scope comes up off the front ring. If your rings are aligned, go on to the next step.
Put the scope in place and tighten the screws just enough to make sure you don't dump your scope on the floor. Move the scope forward and backward, so that your eye naturally falls in the center of the scope's "eye box", the area where the image just nicely fills the ocular lens. Make a small pencil mark on the scope next to a ring, so you can get the scope back into the same position later.
Put the rifle in a bench rest. Put a small level on a flat surface on the rifle and level it front to back. You can get little bubble levels for $1 or so and they work better than the larger ones. Now level the rifle left to right. Then go back and check your front to back level.
Now put the level on the cap over the elevation adjustment, and level the scope left to right without moving the rifle. Tighten either ring just snug enough that the scope won't move.
Assuming you have steel rings, put the other scope ring in place, put a drop of Loctite on the screws, and torque them down to 20 oz inches. Now remove the screws from the first ring, Loctite them, and torque them down to 20 oz inches.
Your scope is now properly mounted, it's positioned for comfortable shooting, you haven't put excess strain on the scope, and it won't shake loose.
It actually takes more time to explain than it does to do.
