I've mounted more than 20 scopes in the last three months. Most for hunting rifles. Some that were previously mounted too but not correctly. First let me start by saying there some tools you will need. If you don't have these tools stop right there and let a professional do the job properly. Here's the long process. Tools:
1). An inch pound torque wrench
2), A lapping bar and lapping compound
3). A leveling system
4) An optical bore sighter or collimator
Start by checking screws for the base to see if they're correct length. Simply done by putting the two front screws on the base or bases one at a time. Start with the very front screw first. After you've torqued the first screw usually 35-40 inch pounds of torque for base screws, try moving the base side to side. If you can do this, the screw is too long and you have made contact with the barrel threads it will cause the screw to loosen as you shoot your rifle. Next remove that screw and thread the next screw on the front and repeat the process above. You will have to trim screws on a grinder if too long or replace if too short. Once you determine both front screws are of proper length, move on to the rear screws to check for proper length. This is easy as you'll be able to remove the bolt and with a flash light see where the screw ends are from underneath. When you have verified all the screws are of proper length, mount the base to the action. If needed apply blue thread locking compound to the screws. Next process is to find the proper orientation of the scope on the receiver. You should have an equal amount of space between the rings and the adjustment turrets and you should also have three to four inches of eye relief at the rear. You can loosely place the top half of one of the scope rings to keep the scope in place while you're doing the orientation. Mark this position with masking tape on the scope tube. Next remove the ring top and scope and lock the bottom half of the scope rings to base using 35-40 inch pounds of torque. You're now ready to check ring alignment with the lapping bar. Apply a small amount of lapping compound to the rings and rock the bar back and forth till you see the bright spots where contact is being made. If these spots are equally consistent in contact there is no need to go any further, level and mount your scope and sight in. In the twenty or more scopes that I recently mounted, all needed further lapping to achieve at least 50% contact. Once done with lapping mark your rings for proper orientation if ever removed. I put a little tic mark with a center punch on the front upper and lower half of the front ring and two tic marks on the upper and lower halves of the rear ring. Next place an orientation level on the base and level the rifle in a vise and lock it. Next place the front level on the barrel and orient it with the rear level on the base. Remove the base level and replace the lower ring halves as they were oriented before. Place the scope on the lower ring halves and then add the upper halves leaving them loose till scope is properly leveled. Place the rear level on the scope elevation turret and orient and level with the level on the barrel. Now tighten the scope rings leaving equal amounts of gap between the ring halves. You can be very exact using a feeler gauge to do this. Now you're ready to bore sight. If you run out of adjustment either vertically or horizontally, you will have to start over and maybe insert shims to successfully bore sight. Scope manufacturers ask that you not tighten scope rings to more than 25 inch pounds as greater torque can result in erratic scope adjustments or damage to scope. I use the Level, level by Wheeler. See video on Midway USA. By the way, the scope brands and ring brands I recently mounted were Nightforce, Leupold, Vortex. There was one AR style rifle and two custom rifles. Glad to answer questions.