I usually mount the scope, shoot it at 25 yards. Put the gun in a vice, put the crosshairs where the bullet went and being sure not to move the gun, adjust the scope to where it will be dead on where you were aiming.
Shoot it once more at 25 yards and if it looks good, move out to 100 yards and tweak it from there.
It has always done well for me and I can usually get the gun sighted in with 1/2 a box of shells and my shoulder still in one piece.
I mount the scope, then use my laser bore sighter to get it on paper. After that is normally only takes one to two shots to get is zero'd at 100 yards. I can also laser bore sight it at 100 yards and never have to shoot it. It will be dead on.
If I understand, you want to know all the steps? First I remove the plug screws, in the reciever, and the front sight if it has one. The plug screws can be used to fill in where the front sight was, sometimes. Some sights will come right off, some have to pushed from left to right, to expose the screws. Then take your scope base and clean it to remove any oil residue, and clean the screws that came with it. I use gun scrubber, by birchwood casey. Don't clean the base with it if it is a glossy base, it can remove blue. Place the base on the receiver. Then get some clear finger nail polish, and apply to the screws, and then attach base. Please don?t use any type of lock tight type product, as you may want to change the scope someday, and you may have to drill out, if it is not removable. Then, place the rear Ring (without the top on of course), on and center the side set screws. Next, place the front ring into the slot sideways. Now you need to find something that has the same radius as your scope, 1" or 30mm. We used an aluminum bar as long as the scope. You place the bar in the front ring and turn the ring into place. Then, take the bar and lay it in the rings to see if they are lined up. You may have to adjust the front ring to make sure the bar sits into both rings, without binding. You can use your scope to test, but don't force it into the rings or you WILL scratch it. Now, put the scope in the rings and very lightly put on the top part of the rings, without the nail polish. You want to be able to twist the scope inside the rings. Take the gun and look through the scope. Are the cross hairs level to YOU YOU YOU.(try to sight something further away and something straight like a wall corner) Is the scope far enough back so that you see a full view with out moving you head too far forward? Now remove the screws one at a time and apply polish, then re-tighten in a criss cross pattern. As far as bore sighting, if you don?t have some type of bore sight (which is a waste of money, unless you can?t look down the bore yourself), remove the bolt, or whatever, then look down the bore at something say 100 yards away. Something circular helps, like a neighbors Christmas reef. Then look through your scope. Move your cross hairs to where the bore is sighted. A vise is almost a necessity. Your done, and your probably closer than a "bore sight". At the range do what Chris said. Put in a vise, shoot once. Move the hairs to the hole, then fire again to check. Now your sighted in with only two rounds. Then bring me some dear meat, as I don?t hunt anymore and have not worked on guns in 12 years. Maybe mot too much has changed, this is just one type of receiver and ring style example. Hope it helps.