Excellent question and topic
It's a HUGE topic. Ironically, it seems not to get nearly as much discussion as it should in the general media.
For example, while doping talk seems to circle endlessly between blood oxygenation and the efficiency of muscular absorption and the classes of drugs and techniques used to boost each, respectively (i.e. blood doping/EPO/etc and insulin/testosterone/steroids/hGH, respectively), you hardly ever hear talk about the "front-end" -- e.g. oxygen intake!
But as you've figured by natural assumption, the greater the oxygen intake, the greater the downstream performance. Which is why ... did you know that nearly 3/4 of the entire professional peloton are ASTHMATICS?!!! Errrrr, or should I say, that nearly 3/4 of the pro peloton have Therapeutic Use Exemptions (TUEs) which permit them to take bronchial steroid agents, otherwise banned from competition, because their doctors have written them up as asthmatics. Yep, a large majority of the pro peloton is doping with bronchial inhalers ... but legally. Of course the entire TUE system is quite a source for discussion for a different post!
At any rate, here are the three simplest things you can do vis a vis breathing:
(1) During exercise, focus consciously on exhaling (deeply/fully). The body's natural mechanisms and the sympathetic nervous system does all the work necessary on inhale, it's just that full clearance of the "dirty" air doesn't happen quite so naturally;
(2) During non-exercise, do breathing exercises that expand the lung and diaphram capacity (in oversimplified terms, yoga-like deep inhalations with full exhalations, then after a deep inhalation, "gulping" little bits more and more and more air to literally stretch the lungs, as well as learning to breath all the way down through the diaphram (note great wind-musicians and singers learn to breath from the diaphram, and that when you see great cyclists, you'll notice the bulge out and contractions in the diaphram when you get a profile view);
(3) During your rides, when you are at an "easy" point, approaching a "hard" pump (i.e. upcoming hill to climb), conciously raise your inhalation/expiration rate (which serves to hyper-oxygenate your blood prior to the big exertion).
Have you ever watched free divers or breath-hold athletes preparing for their efforts? It's worth googling around -- there are video clips you can find on the web. Before a record attempt, these guys will hyperventilate for quite a stretch -- they're doing this to "pre-oxygenate" their blood to the maximum extent possible. (see #3 above). Then when they go to take their "big breath", they take the breath, hold it (using the tongue to seal the airway so no air from the lungs escapes while grabbing another mouthful), then add to it forcibly one mouthful at a time. It looks very much like a "gulping" exercise, like the way a fish out of water looks. They are forcibly expanding the lungs beyond the capacity they reach on a normal inhalation. This is the exercise you can do to expand your lungs (see #2 above).
If you google around, you'll find you can buy breathing devices that are designed to help you expand your basic lung capacity and improve the depth (diaphram) of your breathing. I wouldn't begin to know which to recommend, although it's been on my list to investigate because I'm eventually going to try using one myself.
Good luck and let me know what you decide to try out if you do get one of those devices.
Market Data 
Markets 
AI
