One of the most common comments from runners is the inability to breathe correctly and/or the loss of breath quickly. Many studies of been done on breathing while running. Like any research there are some different opinions, but all agree that a runner has to train their breathing system as they would any other human system.
Some common tips to help:
Many articles recommend breathing through the mouth. Breathing through the mouth increases your oxygen uptake because it simply is the biggest opening to get air into your body.
Breathe using your full chest and abdomen. Using your diaphragm to draw out your stomach will increase your lung capacity.
Run with good posture to keep your lung capacity open. To help, try raising both arms over your head and relax your shoulders. This can help reset your posture. Also, read my previous post on running form. Each of the mentioned schools of thought, in that post, work to improve your running posture.
Find a pattern – 2/2 (in for two steps, out for two steps), 3/2 etc. I've read lots of studies on this, with nothing conclusive other than it helps to have a pattern, any pattern, as long as you stick to it.
Relax! Try dangling the arms. I find if I simply dangle my arms every once in a while on a run, I run more relaxed.
This article from Runner’s World has some good info and techniques: http://www.runnersworld.com/running-tips/how-to-breathe-when-running