During Frank Melloni’s time as an NRA instructor he has found that most people do not understand how to properly affix a scope to their firearm. They fail to realize the error in their ways until they struggle to tighten their groupings on the range.
First, check if the gun’s manufacturer sufficiently tightened the rail mount, which they are notorious for not doing.
Think about what type of shooting you plan to use the system for and determine if a specialized mount would be more suitable for what you intend.
When reattaching the mount, it is important to tighten the screws similar to how you would tighten the bolts on a car’s wheel, working incrementally on opposite bolts. Start by tightening each screw one full rotation and then methodically working diagonally or criss-cross to ensure no one bolt is less tight the others.
Melloni recommends removable thread locker be placed on each screw one at a time after the initial tightening to make the process of removing them easier if the time ever comes.
The fashioning of the actual optic on the mount should also be installed in a similar manner, one full turn on each screw, then opposite incremental tightening, then the application of thread locker.
Once equipped set the eye relief so that you have a full field of vision. It is a best practice to do this at the highest magnification setting as it is the least forgiving. Try a few different shooting positions and if the field of vision isn’t great for one of them you will have to make adjustments unless you have an adjustable stock. If your weapon is bolt-action ensure the bolt handle clears the optic throughout its full movement.
Check for reticle canting, there are products available to solve this problem but they can be expensive. A simple bubble level can be employed to ameliorate any issues.
Lastly apply the same tire criss-cross tightening method to the rim hardware.