Precision Rifle Shooting is just an extension of basic rifle marksmanship. There are 4 fundamentals in marksmanship: Breathing, Aiming, Trigger Squeeze, and Steady Position. Precision rifle shooting is a disciplined sport. Consistency is the key and this relates to the rifle platform, ammunition, and shooter. We want the same thing to happen each and every time we pull the trigger. This can get very detailed, especially when dealing with internal ballistics, so for now I would focus on the basic fundamentals. Fundamentals are what we always fall back on for everything we do, whether or not we are conscience of doing so.
Breathing: Your body has a natural pause - a point where all movement in the body is minimal and we are in a relaxed state. This is on the down breath in our breathing cycle or when we exhale all the air out of our lungs. If we are not relaxed or have to physically hold that rifle on the target - we'll miss. You can comfortably hold this position for up to 10 seconds – depending on the shooter.
Aiming: Aiming is the relationship between your eye, the optic, and the target area. When looking through your optics, you want to have a full field of view. This means that you are looking through your scope and you do not see any black shadows in the viewing area. This is scope shadow and if this is in the viewing area, the focal planes within the optic are not properly aligned and our point of aim will not match up with our point of impact. We will generally impact in the exact opposite point of where we are aiming. Prevent this with proper eye relief. This is the proper placement of your scope on your rifle's optical base and rings. Also with proper eye relief, you should never worry about being hit with your scope during the recoiling of the rifle.
Cheek/Stock Weld: This is the point on the rifle where we rest our face. They call it a weld because your face should be stuck to that stock until that particular shooting iteration is over. When we take our face off of the rifle between shots, we are changing our point of aim - whether it appears that way or not. Remember: Consistency = Accuracy.
Trigger Pull: We want to pull the trigger in a slow/smooth/deliberate manner. One of the posts earlier mentioned that it should surprise you when going off. I disagree. You should know the point that your rifle will allow that firing pin to fall and strike that cartridge's primer. I have been instructing on the larger calibers which offer the higher recoil and I have seen many on the line who didn't know exactly when that rifle was going to fire. They will anticipate the recoil which inadvertently forces their body to react. Now, this will eventually go away as you pull the trigger more but my point is you should know and understand as much as possible when it comes to your rifle/ammunition (your tools), and timing is everything.
Pull the trigger in a slow/smooth/deliberate manner and hold it to the rear until all movement within the rifle has stopped - and then count to 2. We are attempting to prevent any movement caused by pulling the trigger. No matter how fast that powder ignites, pushing that projectile down the bore, we can still affect it while it's inside of the rifle. When we hold the trigger to the rear, it aids in preventing us from hastily "jerking" the trigger. When we are counting to 2, this is our mind forcing our body to react. Unless you are mentally aware of holding that trigger to the rear, you won't. Trust me on that - I see it in every single course. But that's ok, even though we are talking about the fundamentals, or basics, there is still a lot of things going on at once. That is where our mental discipline comes in.
Steady Position: We want to fire this rifle with as steady of a position as possible. Depending on what you are shooting, the recoil phase is one of the most critical. Some of the larger calibers and magnum cartridges will provide you with an extreme recoil pulse that will push the muzzle all over the place. We are looking for consistency and want the projectile to be leaving the muzzle at the same point each time - especially when it comes to shooting for groups. You have 2-3 points of contact with your rifle, depending on how your position is set up. But the 3rd is the most important and that is where the rifle comes into contact with the shooter. It is important to drive the rifle and not let it drive you. The rifle is recoiling to the rear regardless of what you are shooting, and you are that stopping force behind it. I always suggest utilizing some sort of shooting bag that will help absorb that recoil - in conjunction with your body. When we shoot the larger calibers, we use a bag of sand that is slightly larger than the traditional sand sock. I normally take a full sandbag and empty it out to where it is roughly 1/3 full and tape it up so it doesn’t settle as much when you do fire. Then lay your body on it and rest the tip of the butt-stock into it and support the rest of it with your shoulder. It is important to note that you are the one controlling the rifle - not the bag. So keep this in mind when setting up your position. I would assume that your Remington 700 is chambered in .308 WIN, so you don't necessarily need anything that large behind the rifle. The overall goal with this technique is to utilize an additional force to help absorb the full recoil your body will be taking. Tailor this as necessary.
Natural Point of Aim is where the rifle naturally rests in relation to the shooter’s position. You do not want to physically hold your crosshairs on the target. During the recoiling phase, the rifle will move to where it is naturally resting in relation to the shooter’s position. This means you want to be in your relaxed, ready to fire state once your crosshairs are on the desired impact point. To do this, take up a good steady position, point of aim, exhale all of the air out of your lungs, and close your eyes. Hold this relaxed position for a few seconds and then open your eyes. If your crosshairs have not moved, then you and your rifle are utilizing your natural point of aim.
Fundamentals will make or break you in precision shooting, especially at the further distances. I can go on and on about this, but I don’t want to take up the entire board. Just remember this one equation in precision long range shooting: Consistency = Accuracy.
Good luck on your new shooting endeavor.