The purpose of sighting-in (also called 'zero') from a bench rest is to provide a stable and consistent platform for shooting a precise string of shots. It is from the bench that the shooter will be able to tell exactly what the rifle is capable of doing.
Start where you get “on paper” with your rifle and scope firmly mounted and stock screws tight. Remember the scope must be mounted correctly and all must be tight in order to sight in properly. If you do not know how to mount a scope correctly have someone that does help you the first couple of times or have a professional gunsmith do it for you.
Bore sight the rifle, using a bore-sighting device before you fire that first shot from your rifle. This is the first step to getting the bullets to hit on paper. You can also bore sight your rifle the old fashioned way by viewing the target through your rifle barrel, provided that it is a bolt-action rifle. First, make sure that the rifle is unloaded. Next, secure the rifle on a sand bag rest. Then remove the bolt, and sight through the barrel until you have your target centered in the bore. Without moving the rifle, you can then make adjustments on your scope so the cross-hairs are centered on the bulls-eye. Bore-sighting a firearm is the key to getting your first shot “on paper”.
Before you begin the ‘zero’ sight-in phase, remember that if your rifle barrel has been cleaned since firing or it is a brand new rifle (follow proper break-in procedures) to fire a couple of fouling shots before sighting in. Many rifles will not shoot to the same point of impact with a clean, oiled-barrel as they will with a fouled-barrel. You can use these fouling shots to make sure you are “on paper” before beginning the next phase.
Once your scoped rifle has been bore sighted, go to the 100 yard shooting position. Put up a large paper target that is easy to see from this distance. Get yourself really comfortable on the shooting bench, so that you are totally relaxed. It is critical to use a commercial rifle rest or sandbags to support and rest your rifle so there is no movement during this process. Never rest the barrel on a hard surface.
Get to know your rifle and scope and always practice safe shooting. Once you are in a steady sighting-in position on the shooting bench with the rifle pointed at the 100 yard target, load only one round at a time and prepare to shoot.
Using ear and eye protection, place the cross-hairs precisely on the center bulls-eye and proceed to fire the first shot on your new paper target. Now here is the fun part. With the firearm in the “safe mode”, reestablish your rifle so that it is steady on the shooting bench and the cross-hairs are centered on the bulls-eye of the same target. Making sure that you do not move the rifle, have a friend adjust your scopes elevation and windage turrets until the crosshairs are exactly centered on the bullet hole of the shot that you just fired.
Next carefully fire a second shot at the bullseye. If you did not move the rifle while adjusting the scope the second shot should be in the bullseye. In reality most shooters will need a few more shots for small adjustments to get into the center of the bull, but this is a lot faster that most other methods. Of course the final step is to shoot a 3-5 shot group to locate the "exact" center of your group.
Once your rifle is ‘zeroed’, you will have to decide at what distance you want your rifle sighted-in. Remember, when sighting-in, you must "verify" every distance you shoot at, and know for sure what your bullet is doing as it flies through the air, at any given distance. Use the same careful procedure of firing three carefully placed shots, allowing the barrel to cool between shots. The goal is to shoot a two-inch group or better at 200 yards, and a three-inch group or better at 300 yards. When you do. Shoot a final three shot group to make sure everything is consistent and you are Sighted-In!! You should be able to do this with a box of (20) cartridges or less.
The next step in sighting-in for hunting, you will need to get off of the bench and shoot from the field shooting positions, kneeling, sitting, prone, and standing, to see if your rifle will still hold it's zero off of the bench. Be sure to hold and grip your rifle the exact same way, throughout all of the shooting positions to ensure same pressure and same point of impact, confirming your accuracy in each of the positions. Set up a picture target (card-board cut-out) of a deer or whatever animal you're hunting at 200 or 300 yards (your zero) and carefully shoot a three shot group. Your shots should be evenly grouped on your point of aim. If the groups are much larger than MOA, think about trigger control and proper position and try again.
If you have cleaned your rifle five rounds ago or less do not clean your rifle anymore if you are going hunting, allow your rifle barrel to be "seasoned" with some "fouling" shots from when you were last shooting well. Carefully place your rifle in it's travel case, and be careful not to drop it during your transport to your hunting destination. And ALWAYS shoot your rifle at your hunt destination, to CONFIRM your sighting-in process at the place where you will do your hunting.