There has been some pretty good information posted, so rather than repeat it, I will proceed with some advice that I didn't see posted related to rifle handling and shooting.
You have to learn how to quickly assume field positions for shots at longer ranges, and how to shoot-off hand when the range or time is short. After the shot, do not lower the rifle, work the bolt at your shoulder as quickly and as forcefully as you can; you won't hurt the rifle, and forceful operation is the only sure operation. This will provide you with a faster follow up shot if you require one, and does no harm if you don't need to shoot again.
If you shoot from the bench to familiar yourself with your rifle and to sight in, thats fine, but once you are familiar with the rifle, get off the damn bench and start shooting from field positions. The challenge here is to spend the time on the positions that cause you the most trouble. If you can shoot at all you can shoot prone, and shooting prone has its place, but you need to allow for as many rounds from sitting, kneeling and off hand as you do from prone. It won't take long to determine that your maximum range is different from each position. Don't get caught up on shooting groups. You don't shoot groups on game; on game you seldom have more than 2 shots, so get in the habit of firing a carefully aimed shot followed by a rapid follow-up shot. Your maximum range is when your 2 shots impact on the target 6" from your point of aim. When your impacts exceed 6" from your point of aim, you either have to work on improving your shooting at that range, or work closer. Get used to judging range by the size of your target against your sight. If you typically fire at a 8.5"X11" target, pay attention to how that appears against your sights at various ranges, then you can say, a deer has about a 12" kill zone, so what range do I recognize that as?
Learn how to acquire and check you natural point of aim. You won't have time to do this in the field, but on the range if you learn the feel, it will be approximated in the field. Natural point of aim is checked by closing when you have a sight picture, then close your eyes and allow your muscles to go slack. When you open your eyes, if your your sights should still be on target, if the sights have swung off target your position needs to be adjusted, adjustments should be made in very small incriminates.
When shooting from supported positions, that is any position where your elbows are placed on a firm surface, get in the habit of slinging up. The positive pressure that is created from the front sling swivel to your support arm anchors the rifle, and increases the chances of a hit by approximately 30%. I prefer a sling that is purposely designed fro this type of shooting like a Ching Sling or a Safari Ching Sling, but a carry strap used as a hasty sling works to a point. There has been some debate as to the usefulness of slinging up for off hand shots, but I contend it has not advantage and is slower where the off-hand shot often must be made quickly.
When shooting off-hand a hard flex of your stomach muscles causes the sight to momentarily freeze in position, from here on it is a timing problem to achieve a compressed surprise break before the sights once again wander off target.
When you are training, always challenge yourself. You should never fire a shot that doesn't teach you something. When you think you have position shooting down, reduce the time interval it takes you to fire. Make a short run prior to shooting so that you are forced to shoot when out of breath. Observe what happens to your group size and the position of the impacts on the target as you shoot at longer ranges. Be creative, work out how to run moving target scenarios. By the way the most difficult moving target is not one that moves across your field of view, the most difficult target is one that moves rapidly towards you, as the tendency is to shoot where it was. The easiest was to solve the problem is to shoot from a lower position like kneeling to put the trajectory of the bullet on the same plane as the length of the target.
Your rifle probably has a two stage trigger, which means that there is some slack that must be taken up before you can feel the sear. When the trigger breaks it must surprise you, that is surprise you, not startle you. You know the trigger will break, just not when, so that is an open ended surprise break. A compressed surprise break is when the sear breaks within a compressed period of time, typically 3-5 seconds, less in an emergency, more when circumstances allow.
If you are using iron sights, you align the rear and front sight on the target to acquire your sight picture. Once your sight picture is acquired, shift your focus to the front sight allowing the rear sight and target to blur. Objects at different distances cannot be held in simultaneous focus, so your focus belongs on that front sight.
Hope this helps.
