Proper breathing control is important for a successful stretch. Proper breathing helps to relax the body, increases blood flow throughout the body, and helps to mechanically remove lactic acid and other by-products of exercise.
You should be taking slow, relaxed breaths when you stretch, trying to exhale as the muscle is stretching. Some even recommend increasing the intensity of the stretch only while exhaling, holding the stretch in its current position at all other times (this doesn't apply to isometric stretching).
The proper way to breathe is to inhale slowly through the nose, expanding the abdomen (not the chest); hold the breath a moment; then exhale slowly through the nose or mouth. Inhaling through the nose has several purposes including cleaning the air and insuring proper temperature and humidity for oxygen transfer into the lungs. The breath should be natural and the diaphragm and abdomen should remain soft. There should be no force of the breath. Some experts seem to prefer exhaling through the nose (as opposed to through the mouth) saying that exhaling through the mouth causes depression on the heart and that problems will ensue over the long term.
The rate of breathing should be controlled through the use of the glottis in the back of the throat. This produces a very soft "hm-m-m-mn" sound inside the throat as opposed to a sniffing sound in the nasal sinuses. The exhalation should be controlled in a similar manner, but if you are exhaling through the mouth, it should be with more of an "ah-h-h-h-h" sound, like a sigh of relief.
As you breathe in, the diaphragm presses downward on the internal organs and their associated blood vessels, squeezing the blood out of them. As you exhale, the abdomen, its organs and muscles, and their blood vessels flood with new blood. This rhythmic contraction and expansion of the abdominal blood vessels is partially responsible for the circulation of blood in the body. Also, the rhythmic pumping action helps to remove waste products from the muscles in the torso. This pumping action is referred to as the respiratory pump. The respiratory pump is important during stretching because increased blood flow to the stretched muscles improves their elasticity, and increases the rate at which lactic acid is purged from them.