When you install a scope on a rifle, it's a good idea to boresight it. Boresighting insures that the optics are aligned with the bore of the rifle. Boresighting doesn't take the place of zeroing the rifle with good ammunition, but it will save ammunition when zeroing the rifle.
One way to get the scope looking where the barrel looks is with a commercial boresight device like this one. You can spend a little or you can spend a lot.
Or you can go out into the front yard, set up a bench and look down the barrel, find a suitable target and adjust the scope to that target. Being the frugal sort that I am, I've never bought the device. I've always set up a bench in the front yard.
This morning I set up the bench and boresighted the .30-06 with the Weaver scope. My aiming point is a mailbox about a hundred yards from my house.
That mailbox has a good aiming point in the cross between the horizontal and vertical timbers. With the bolt out of the rifle, it was easy to look down the barrel and center that aiming point in the bore. I had mounted the scope on the rifle and the initial sighting showed that the scope was fairly well centered, but was off about six inches to the left. I easily brought that into line with the windage adjustment.
Now I know that the rifle should shoot close to where it looks and when I get some ammo assembled for it, conducting a proper zero at a proper range should be much easier. The rifle is boresighted with the scope.
Of course, there was no ammo anywhere close for that rifle, and the rifle itself was disassembled. I purposely took the bolt out and left it on the kitchen table.
The truly amazing thing was that this was a standard Saturday morning in a standard Louisiana subdivision. People were moving about and working in their yards. No one thought that there was anything odd about a man with a scoped rifle sitting at a bench in the driveway.
Ain't life grand?