I should add that a scope doesn't make a weapon more or less accurate. The weapon's accuracy will be determined by the condition and quality of the weapon and the consistancy of the load. You, as the shooter, will have more to do with where the bullet lands than any other factor.
For iron sights (skip to 4 when using a riflescope):
1) Stock Weld. You need to have a consistant stock weld (where your cheek comes into contact with the stock). A lot of shooters would place a strip of adhesive tape on the stock right where their cheek would come into contact with it.
2) Sight Alignment. The tip of the front sight post must be perfectly centered (horizontally and vertically) in the rear sight aperature. This has a more pronounced effect than sight picture (Item 3 below). If you are having a hard time consistantly hitting paper this is the likely culprit.
3) Sight Picture. With the proper sight alignment, place the tip of the front sight post in the desired point of impact. You should be focused on the front sight post so that both the rear sight aperature and the bulls-eye will be out of focus (blurry). You can tell when someone is making the common mistake of focusing on the target because they would be breaking paper all around the bulls-eye. We called this "chasing the bull".
While a scope will relieve you of the above responsibilities, the following needs to be followed for all shooters:
4) Verticle alignment of the rifle. Do NOT cant your rifle to the left or the right. It will skew your sight adjustments (windage and elevation). This will be most noticeable at long distances. If you have a real bad time with this, I think they have a level you can attach to your rifle to help you.
5) Breathing control. Take in a breath, slowly release half of it, and take your shot. Be patient, if you can't get a steady shot, put the weapon on safe and relax.
6) Trigger squeeze. Take up slack and slowly squeeze the trigger until the rifle fires. I have seen people wait until they have perfect sight picture and quickly jerk the trigger before they lose it. You can see evidence of this by a very pronounced vertical impact pattern or worse yet, shooting over the target.
7) Let the rifle surprize you when it goes off. Some people anticipate the weapon discharging and flinch or throw their shoulder into the rifle. We called this "bucking" ... it will affect your accuracy as much as poor sight alignment with the round hitting the dirt in front of the target as the final result.
Learn how to use and adjust your sling to help keep you in a tight (and sometimes painful) shooting position. Mark the keeper on your sling so that you can easily return it to the same position. Consistancy is the name of the game if you desire to become a superior marksmen. Keep a log book detailing each shot that you take. Note the date, time, weather, wind direction, velocity, clouds, temperature, and distance to the target. Mark both where you think that you hit the target and where you actually hit. If you think that you jerked the trigger on a particular round, note that. Write down any sight adjustments. When firing off-hand (standing), your sights will naturally adopt a figure 8 pattern. I am told this is because of the beating of your heart. If you try to control it, you will just get the shakes and tremors ... worse than the original figure 8 problem. When firing prone (laying down), do not rest the barrel on any rest, log, or sandbag. Even though the bull-eye is printed flat on the target, it will cast a shadow on a sunny day - don't ask me why.
Semper Fi