The ASA has meticulous rules for swimming each of the major competitive strokes: breaststroke, butterfly, backstroke and freestyle. For the full rules, go to the link listed as Reference 2. The rules cover body position at the start, the exact permissible nature of the stroke, the allowed foot and leg action during kicks, and the way in which turns and finishes should be executed.
Start: The breaststroke uses the front start.
Stroke: All strokes must take place on the breast, with no rolling onto the back permitted. The stroke cycle is one arm stroke and one leg kick--in that order. The hands are pushed forward together, and the elbows must be underwater, except for the turn and the stroke just before it. The hands are brought back in or under the surface of the water, and must not go beyond the hip line, except during the first start and the first stroke after each turn. During each stroke sequence, some part of the swimmer's head must break the surface.
Kick: After the start, and after each turn, a single butterfly kick is permitted. After that, all leg movements must be simultaneous. Scissors, flutter or downward butterfly kicks are not allowed in this stroke, though breaking the surface of the water is. The feet must be turned outwards during the propulsive part of the kick.
Turns and Finish: The touch at each turn and the finish must be made with both hands simultaneously. The head must break the water at some point during the last complete or incomplete stroke cycle before the touch.
Start: The butterfly stroke uses the front start.
Stroke: After the start and after each turn, the shoulders must be at or past the vertical toward the breast. One or more leg kicks, but only one arm pull under water, is allowed. It is not permitted to be completely submerged for more than 16.4 yards after the start and after each turn. By that point, the head must have broken the surface. From the beginning of the first arm pull, the body is kept on the breast. Both arms must be brought forward over the water and pulled back simultaneously.
Kick: All up and down movements of the legs and feet must be simultaneous. No scissors or breaststroke kicks are permitted.
Turns and Finish: The touch shall be made with both hands simultaneously at, above, or below the water surface. Once the touch is made, any turn is allowed. The shoulders must be at or past the vertical toward the breast when the swimmer leaves the wall. The same rule applies to the finish as to the touch.
Start: Swimmers must face the start end, with both hands on either the gutter or the starting grips. Putting the feet or toes on the gutter is prohibited.
Stroke: The backstroke is swum entirely on the back except during the turn and for a distance up to 16.4 yards after the turn. Some part of the swimmer must be above the water at all times except during these instances.
Turns and Finish: Some part of the body must touch the wall at every turn. During
the turn the shoulders may be turned past the vertical toward the breast after which a continuous single arm pull or a continuous simultaneous double arm pull may be used to initiate the turn. The swimmer must have returned to a position on the back upon leaving the wall. At the finish, the swimmer must touch the wall on his back.
Start: Freestyle uses the front start.
Stroke: Any stroke may be used, though some part of the body must break the water at all times except during the turn and for a distance of 16.4 yards afterwards. Any established kicks may be used.
Turns and Finish: Some part of the body must touch the wall at each turn, and at the finish (after completing the required distance).