The shooting plain of the rifle and the sight plain of the scope must be in concert (parrallel left nad right). If they aren't, it will cause the bullet to drift left or right past the zero point. The scope must be plummed to a plumb reciecer. If it isn't the shooting plain and the sight plain are not syncronized.
IMO the best way to do that is as folows...
The last scope I bought, the dealer put it on for me although I would have done it myself. I'm glad he did, because I watched and learned how to do it accurately. He used loctite on all the screws. Here's what he did.
1) placed the rifle in a rest and put a small magnetic level on the receiver's scope base and leveed it, right - left, not front - back..
2) put a level glued to a small round magnet on the muzzle and level that level to the one on the receiver.
3) removed the level from the reciever and attached the bases and bottom ring halves, using loctite.
4) placed the scope in the bottom ring halves, and attached the top halves of the rings, but not tight.
5) took the rifle and gave it to me to hold to adjust scope forward/backward to fit my eye relief. Need to be careful here, that the level on the muzzle is not disturbed.
6) put the rifle back in the rest and leveled it usine the level attached magmetically to the muzzle.
7) took the level used to level the receiver and put it on the top turret of the scope and leveled the scope in the rings, then double checked the muzzle level again.
8) tightened down the ring screws incrementally. Good to go.
A good way to double check this is to align your verticle reticle on a verticle line some distance away, the farther the better, then look down your bore with bolt removed and see if the distant verticle line bisects your bore.