Take off the top of the scope rings, you don't say what kind of rifle, but lock the barrel down, with the bolt removed, and pick an object about 100yds away, (I use a neighbor's basket ball goal) and sight through the barrel, centering the bore on the object.
Take the scope and placing the objective end against a mirror, by looking into the scope you will see how far off your reticle is (should see two sets of crosshairs) and turn the adjustment knobs to re-center the reticle (all lines should appear as one, each direction), then place the scope back in your ring bottoms and see how far out of alignment the scope is. If it is properly aligned, your sight picture should be the same between the bore and the scope picture.
You may need to adjust the scope ring mounts right, left, up or down (they may be made for front/rear application and be on backwards). If they don't have adjustment, you may need new rings.
Make what ever adjustments necessary to the mounts to have them lined up with your bore sight picture and then tighten the top of the rings back on the scope.
When you can get to the range, the scope should need only minor adjustment for point of impact. Use new ammunition for testing. While 'old' factory ammo should be good, reloaded ammo can have a lot of variances, especially if they are not your loads.
If possible, find a way to tie your rifle down in the bags or shooting rest to remove as much human contact as possible (I use a Caldwell Lead Sled). Preferably your only contact with the firearm will be your trigger finger after you get the reticle centered in the 'bull'.
If the scope is good at this point, on a separate target, fire one round at the bullseye, run the elevation up 8 clicks and right 8 clicks, keeping the crosshairs on the bullseye for each of the next shots, fire a shot. Move the windage left 16 clicks, fire one shot, then elevation down 16 clicks, fire the shot, windage right 16 clicks, fire the shot and then left 8 clicks and up 8 clicks and fire the shot... Your last shot should be really close to the first round point of impact and the four corner shots should be pretty much a perfect square.
If this occurs, your scope is in good shape and you should be in pretty good shape for the future. If the scope does not return to center, or the corner impacts are not pretty much square, call the manufacturer.. If you have run the above exercise, they will need that information to take any claim in a credible light. It's always easy for them to claim "Shooter Error"..
