There are three steps to the arm movement: outsweep, insweep, and recovery. The movement starts with the outsweep. From the initial position, the hands sink a little bit down and the palms face inward, and the hands rotate outward and move apart. During the outsweep the arms stay almost straight and parallel to the surface. The outsweep is followed by the insweep, where the hands point down and push the water backwards. The elbows stay in the horizontal plane through the shoulders. The hands push back until approximately the vertical plane through the shoulders. At the end of the insweep the hands come together with facing palms in front of the chest and the elbows are at the side at the body. In the recovery phase the hands are moved forward again into the initial position under water. The entire arm stroke starts slowly, increases speed to the peak arm movement speed in the insweep phase, and slows down again during recovery. The goal is to produce maximum thrust during the insweep phase, and minimum drag during the recovery phase.
As a variant, it is possible to recover the arms over water. This reduces drag, but requires more power. Some competitive swimmers use this variant in competition.
Another variant is the underwater pull-down, similar to the push phase of a butterfly stroke. This stroke continues the insweep phase and pushes the hands all the way to the back to the sides of the hip. This greatly increases the push from one stroke, but also makes recovery more difficult. This style is well suited for underwater swimming. However, FINA allows this stroke only for the first stroke after the start and each turn. In late 2005, FINA has also introduced a new rule which allows you to perform a single downward kick after the push off the wall.
[edit]Tips
Arms start slowly and speed up during the phases, similar to a motorcycle accelerating after standing on a red light. The arms are never paused until they reach the front and the swimmer is in the glide. A more detailed explanation is here. in this detailed arm stroke description. Catch
Arm action begins with the arms fully extended out in front, fingers and hands together. Hands pitch outwards and downwards to an angle of about 45 degrees at the start of the catch phase. Arms pull outwards and downwards until they are approximately shoulder width apart. Elbows begin to bend and shoulders roll inwards at the end of the catch phase.
Propulsive phase
Arms sweep downwards and inwards and the hands pull to their deepest point. Elbows bend to 90 degrees and remain high. At the end of the down sweep, the hands sweep inwards and slightly upwards. Elbows tuck into the sides as the hands are pulled inwards towards the chest and the chin.
Recovery
Hands recover by stretching forwards in a streamlined position. Hands recover under, on or over the water surface, depending on the style of stroke to be taught.

Most people find the arm action easier than the legs. Have your arms stretched out in front of you, push your arms away from each other to make a full circle and stretch them out again, to repeat the circle. Your hands should stay in front of your shoulders. So if you can always see your hands, you're arm action is on the right tracks. There should be very little splashing, if any, caused by your arms. As your arms are stretching out to do their circles your legs should be pushing back to start their movement.
To start breaststroke:
Begin with a torpedo position.

After you have gone about a meter pull you arms back to about your shoulders.

Then bring your hands under your chest.

Now push your hands back out to a torpedo position again.

This is the basic breaststroke.

Once you have got the hang of that you need to learn to lift your head. You do this in the pulling of your hands back to your shoulders. Basically you pull harder and as you pull you lift your head up.

Don't bother about taking a breath at this point. You almost certainly will have your head in the wrong position. We'll talk about breathing in your breaststroke next time. Concentrate on getting you arm action right.
Start with arms extended, shoulders under the water out in a Breaststroke streamlined position (arms extended thumbs down backs of hands make a ‘V’), eyes to the pool floor