Breathing seems like it would come naturally when running, but I am often surprised by the number of runners I see that struggle with this. The two mistakes I see most often are:
1. Hyperventilating (breathing to quickly)
Though it may seem counter intuitive, breathing faster does not provide the body with more oxygen. this is because it takes a moment for your lungs to exchange inhaled oxygen for exhaled co2. The runner that is breathing rapidly is inhaling oxygen, and exhaling the same oxygen before the exchange has occurred.
2. holding your breath.
The body needs oxygen for aerobic activity, in fact that is the very definition of aerobic activity. Though your body will eventually make you breath, or stop running, or both, be careful you are not holding your breath at the start of the race due to pre race jitters. Everytime you step to the line take in a few deep rythmic breaths. this will not only ensure you are not holding your breath, but will also help to calm those pre race jitter.
Proper breathing while Running
Try to take deep slow rhythmic breaths. It may at some point feel like you should increase your rate of respiration, but remember, your primary concern here is not how many breaths you take, but how much oxygen you body is getting.