The diaphragm is the muscle located under the lungs that is designated to expand the lungs and bring air into them.
To breathe efficiently by using the diaphragm effectively, think about drawing air into the bottom third of your lungs as you expand your belly like a balloon.
Try doing this while inhaling through your nose and you'll notice a relaxing sensation throughout your body.
Take a few moments before each workout to sit quietly and practice breathing through your nose and with the diaphragm. This will start your workout in the right frame of mind and with correct breathing.
Keep reminding yourself how to breathe with the diaphragm throughout your workout, and return to it if you fall back on incorrect breathing.
Another breathing aid is to focus on exhaling forcefully during climbing and hard efforts. Once you've developed the habit of filling your lungs completely by breathing with the diaphragm, your body will take care of the inhaling portion on its own.
By forcing the air out of your lungs you'll develop a more complete, efficient breathing cycle. Short, shallow breaths don't completely fill or empty the lungs and will dilute incoming oxygen with carbon dioxide.
I've also found that airflow improves if I drop my jaw and open my mouth in an oval shape (vertically) during hard efforts.
Thomas Chapple is a licensed Elite Level USA Cycling coach, certified USA Triathlon coach and Ultrafit Associates coach. He coaches regional and nationally competitive athletes and has competed at the national level in downhill mountain-bike racing.