There are a number of points which come to mind, most of which are the basis of basic marksmanship which are covered by the acronym BRASS which stands for; breath, relax, aim, slack, squeeze.
Breath, you must breath for each shot you make. If you rush the shot because you’re lungs are screaming for air, your focus will blur and you will probably yank the trigger disrupting your aim. When you breath pay attention to your natural respiratory pause, you will find that it is repeatable, and that your lungs have the same amount of air in them each time you transition from inhaling to exhaling. Concentrate on making a surprise break during that natural respiratory pause. Some will insist on breathing out all the air in your lungs and that this results in a more stable position. For them it might, but it significantly reduces the amount of time before your vision begins to blur.
Relax; your body must be relaxed. If you are in a proper position, your skeleton supports the rifle not your muscles. You should be able to close your eyes and allow your muscles to go limp, without finding that your sights having moved off target when you open your eyes. If you find that you have to rush the shot due to lack of air, you have lost breath and relax, so start over.
Aim, aiming requires a number of steps. First acquire the sight picture, that is you place the sights on the center of the target. Next you put the front and rear sight in proper relationship to one another, taking care that together they are properly aligned on the center of the target. Finally, shift your focus to the front sight and hold it there, and nowhere else, until the shot is made.
Slack, simply refers to taking the slack out of a two stage military trigger. You press the trigger until you feel the resistance of the sear. From this point it takes little effort to brake the shot.
Squeeze, is a term I dislike as it suggests something we don't mean. Consider a baby squeezing your finger, it grasps your finger and squeezes with his whole hand. That is not what we do on the trigger. You hold the wrist of the stock in a firm handshake grip, and only your trigger finger moves; first through the slack stage of the trigger than through the release of the sear. You make contact with the trigger using the first pad of your index finger, and then you add pressure to the trigger until at some time it brakes. That brake should come as a surprise. With practice it can be compressed into a very short time frame, but it should still be a surprise. That is it should surprise you, not startle you. When the sear brakes, continue to add pressure to the trigger until the gun has settled back from the recoil. That is called follow through. An easy exercise you can conduct at home is to balance a coin, start with a quarter then work your way to a dime, on top of the barrel, near the front sight. You should be able to press the trigger until the contact with the sear brakes and not disturb the coin when the striker falls.
When shooting at paper, work on establishing and checking your natural point of aim. That is where you hold the rifle on target and when you relax your muscles the sights do not swing off target. Small corrections are made to your position until this is achieved. The test as described earlier is to close your eyes, allow your muscles to go slack then open your eyes to determine if the sights have swung off target. Natural point of aim is dependent of a solid supported position, so begin with working on your positions then work your way through the BRASS acronym. Once you can quickly and acquire your natural point of aim by feel, shots in the field on live targets become easier.