I'm an ex gunsmith. Fitted lots of scopes. I confirm Publius's instruction that the first move is to centre the reticle by adjusting fully one way, fully the other, then halfway back. Same for verticle. That's necessary because you need adequate left/right and up/down adjustment after everything is tightened up. Actually, its all left/right, the up/down is much less important because it is in the lateral plane that most errors in the mounts occur.
As publius says, take it easy when you get near the extreme left or right adjustment. Most scopes have clicks, and get noticeably tighter near the limits of their adjustment. Stop when you feel it getting stiffer, don't push it. Also be aware that some scopes don't have click adjustments. Leupold is a smooth movement without clicks, and comes to a dead stop at the end.
Now, here's where it gets interesting. Scope rings are never, and I mean NEVER, properly aligned unless they have been lapped in position. That's because of normal tolerances in the manufacture of rifles and bases and rings. I never saw any that were not out to some extent. The result is that the ring grips the scope by its edges, and no matter how tight you cinch them up, there is not enough grip with that point contact to prevent the scope from shifting in recoil.
When the scope shifts the ring can scrape the finish off the scope, and I have seen expensive scopes that were badly disfigured in that way. I've even seen scopes that were slightly dented by their rings.
What you want is rings that grip the scope tube exactly and evenly over the whole inner surface of the ring. You can only get that if they are exactly aligned, and you can only get that by lapping them. You need a precision machined rod about twelve inches long. For a one inch tube scope that's a one inch rod. Apply lapping compound, 600 grit is about right, and lap the rings back and forth. You can see when the job is done because it progressively removes the blue as it cuts.
I have a simpler method that is theoretically less precise but works well. I machine a rod 24.80m dia. I wrap a single thickness of wet or dry around it, which brings it to 25.40mm (one inch) and polish the rings with it. I start with 180 or 220 grit for rapid metal removal, and finish with 320. An finally, a coat of cold blue. I assure you that, when the scope is dropped in, that bank vault-like feel of 100% solid fit can be felt. I have set up some heavy recoiling rifles this way and never had one come back.
How far out are the rings, typically ? One to three thousandths, as close as I could tell because it is not easy to measure. Six thou in the worst cases. But that's all it takes for there to be nothing more than point contact at the edge of the ring, and effectively no grip.
Even today, despite the absolute proof that rings are always out, and the necessity for this procedure, it is done only by a tiny minority of gunsmiths or dealers. Why ? I found that it is not believed until I prove it in front of their eyes.
Which brings me neatly to the pointed test rods. Forget them. As Publius says, if the points don't line up you know you have misalignment. But they don't tell you how much or which way. If they don't line up left/right, it doesn't tell you whether one ring is left and one right, or whether they are out left or right by different amounts. And if the points do line up, both rings could be out in the same direction by an equal amount. My argument is that the ringswill ALWAYS be out, without exception, so why bother with test devices that don't tell you anything, just lap 'em as a matter of routine, because you'll always have to.
I made my own test bars, because they are useful for just one thing, showing the customers who just don't believe it until they see it.
Shimming is another matter. Shouldn't be necessary unless the bases or rings are not right for the rifle. But it is a legitimate way of getting the bases more or less right, and I have to concede that some military rifles like the ubiquitous M98 can have enough variance in receiver height to require shims. You can buy them from Brownells, but most gunsmiths keep some shimstock, and I used to cut my own.
Just to further illustrate, for the sake of interest, the sort of thing that gunsmiths encounter, I had two rifles with Weaver bases and rings, that would not shoot to point of aim at max lateral scope adjustment. As you know, Weaver mounts do not permit lateral adjustment. One rifle was corrected by reversing front and back rings, the other by turning the rings 180 degrees. That tells us that some things are fixed by simple methods, and that manufacturing tolerances can make that much difference.
