One step I include that I didn't see mentioned. I place a 4 foot level or any other straight edge along the scope base (or bases if two piece) to ensure the scope bases are in alignment with the barreled action. I am ensuring that the straight edge has the same amount of offset - left to right - from the center line of the bore at the muzzle, prior to securing the scope base to the rifle receiver. I had one receiver where the one-piece base was pointed cattywompus. I had to use a Dremel tool to enlarge the sides of the screw mounting holes in the base in order to align the base to the bore of the rifle. Only then was the scope base able to be mounted parallel to, and in left-right alignment with, the bore at the muzzle.
In addition, I use a 'Vertical Reticle Instrument' manufactured by EXD Engineering. I purchased mine through Brownells. Part number 289-100-000
EXD ENGINEERING VERTICAL RETICLE INSTRUMENT - Brownells
This tool helps to ensure that the center-line of the scope is positioned directly over the center-line of the bore, at the same time the scope reticle is turned to vertical with the plumb bob string. I try to set my plumb bob up 50 or more yards from the scope. It just seems easier to see the plumb bob string. This tool rest on the barrel and the objective end of the scope tube - concurrently, and then the user tilts the rifle until the bubble level indicates the scope tube and barrel are plumb with the earth. After this is achieved, the scope is turned in the rings until the crosshair is vertical with the plumb bob string, at which point the ring screws are snugged down (while ensuring alignment with the plumb bob string is maintained). And then finally, an anti-cant scope level device is mounted while everything is confirmed to be properly aligned - parallel with gravity.
This method works slicker than snot. And provides high assurance of a correctly mounted scope.