A breathing stroke cycle in freestyle is identical to a non-breathing cycle with one exception. A breathing cycle includes enough head rotation to position the mouth just above the surface to allow breathing. Rotating the head to breathe synchronises best with the Finish phase of the arm on the breathing side. Inhalation occurs during the Recovery phase. As the arm moves past the shoulders to begin the Entry phase, the head rotates back to the non-breathing position. You should exhale the entire time your head is in the non-breathing position. In doing so, you will be able to inhale more quickly and efficiently.
It is most comfortable to breathe when the least amount of head rotation (with respect to the body) is necessary. The head should begin to turn when the torso is rotated the most, at the end of the Finish phase / start of the Recovery phase. You should only rotate your head just enough so that the side of your mouth is breaking the surface of the water. Many (actually, most) swimmers rotate their heads too much. Your lower goggle should still be submerged in the water, creating a split-screen effect. The head should return to its neutral position as the hand enters the water for the Entry phase - beginning the stroke cycle all over again.
Breathing to the same side on every inhalation, should not generate extra resistance and negatively impact performance. It will in fact allow you to uptake more oxygen per minute, therefore increasing performance when the oxygen demand is high. Nevertheless, breathing bilaterally can certainly help swimmers achieve a more symmetrical stroke, so at THP we advocate implementing it into all of the easy sections of your swim sessions. In the open water in particular - being able to breathe to both sides is an absolutely essential skill. When you experience choppy conditions or glare from the sun, being able to turn your head to breathe from either side - is a valuable skill to possess.
Turn head at Finish phase when rotation is at its greatest
Only turn enough to reveal side of mouth
Lower goggle remains submerged
Head returns to neutral as hand enters the water