Breast Stroke
Contrary to popular belief breaststroke is probably the most difficult of all strokes to master. The flat position of your body makes you like a barge moving through water, so to move fast you need to make yourself as streamlined as possible and this makes the timing of the stroke difficult to get right.

If we look at a good breaststroker in action we can see the main elements of the stroke and the relative timing of each movement: 
At the end/beginning of a stroke the legs are snapped together with feet pointed. To begin the stroke the hands scull out beyond shoulder width with no propulsion, as any pressure would only produce upward movement . Then the elbows bend so you can use the whole of the lower arm and hand to hold the water.  Propulsion comes by holding the elbows high and moving the hands round and in, while the legs remain streamlined. 
The arms accelerate throughout the stroke and when the elbows are level ... with the chest both the hands and the elbows are driven together.  When the hands meet the legs begin to break at the knee and the feet are drawn towards  the buttocks. The toes turn in towards each other and the hands extend in a streamlined 
position both forward and downwards. The feet remain pointing back until the arms are fully extended . At which point the feet are turned out to present the instep to the water behind and are ..... driven backwards at a very fast rate. If you trace this movement the actual shape they would draw would be a  narrow oval. The feet and legs are snapped together while the arms remained streamlined.
Two areas in breast stroke cause swimmers problems. The first is how the legs and feet should be positioned to move backwards and the second is how wide and far back should you move your arms?

From the above sequence you can see that the hands never come back beyond the chest line, the first two pictures in the second row illustrates the curvature of the back and the hand position nicely. However, they don't illustrate the width of the arms or the track the legs and feet follow during the stroke so we'll use TriMan to illustrate these:
As the hands extend into a streamlined position the feet are pulled towards the buttocks. Your toes firstly point toe to toe and as they approach the bum they are turned to present as much of the instep as possible to the rear. From that point the head and arms are pushed forward and down while the legs are propelled backwards tracing a narrow oval shape. During the kick your knees should be kept as close together as is comfortably possible. In the final phase of the kick the toes are pointed in line with the legs (plantar flexed). At the same time the knees and feet are driven forcefully together and the whole body should have moved into a very streamlined position.

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During the kicking phase of the stroke the arms have little or no propulsive role. Part of the reason for this is that, to be effective, the kick should happen while the body is as streamlined as possible otherwise the resistance the body creates against the water immediately stops any forward movement. Again we'll turn to TriMan to illustrate the correct motion:
At the end of the kick phase of the stroke the arms and body should be as streamlined as possible. As your speed slows you scull your arms out beyond shoulder width. None of this is propulsive (i.e. it doesn't produce any force against the water) if it does then it will only result in the body lifting in the water  as the propulsive force will be downward.
From that point the hands drop in a circular motion while the elbows remain high, almost on the surface of the water. As the hands accelerate towards each other both the hands and the fore arms are used to produce propulsion. This movement lifts the body and the elbows begin to drop and snap together. Once joined the hands drive upwards in front of your face and then the elbows are squeezed together as your hands move both forward and downward into the streamlined position.
Of all the major competitive strokes the leg kick in breast stroke is the most propulsive, so kick sets during training are important to build strength and endurance. However, the stroke is tiring when performed correctly and it is unlikely that any training session would contain more than 25% of full stroke breast stroke.