This is an excellent question, as many people have misconceptions about how to breathe when running. You should breathe through both your mouth and nose when you're running. Your muscles need oxygen to keep moving and your nose simply can't deliver enough.

Make sure you're breathing more from your diaphragm, or belly, not from your chest -- that's too shallow. Deep belly breathing allows you to take in more air, which can also help prevent side stitches.

You should exhale through your mouth and try to focus on exhaling fully, which will remove more carbon dioxide and also help you inhale more deeply.