Air Rifle, Pistol and Archery Training Tips

The Six Fundamentals of Shooting

Shooting Stance 

The feet and body are turned so that the body faces at least 90 degrees
away from the target and the left side is pointed towards the target.
The feet are shoulder width apart. Both legs and knees are straight.
However, the muscles in the legs must be relaxed, not tense.
The left arm must rest on the left side, directly under the rifle. The elbow can rest on the hip, or the arm can rest on the side, but it must always be directly under the rifle. The rifle rests on the left hand. Most
shooters make a fist with their hand and rest the rifle on the fist. There are different support hand positions that are correct for different individuals. The rifle should be placed fairly high in the shoulder so that the head can be kept nearly erect. 

The website Target Techniques explains this further here

Matt Emmons, picture from eley.co.uk. Normal stance.
Olympic Shooter Ivana Maksimovic

Grip Technique

The first step to the trigger finger being able to properly pull the trigger is to ensure that the grip on the rifle is correct.

For rifles this means that the trigger hand is firmly gripped around the stock applying slight rearward pressure into the shoulder and the support hand is loosely gripping the fore end of the rifle, supporting the rifle.