For the non yoga
practitioner who is still interested in achieving the benefits of yogic breathing; here's what I think is the easiest way to perform yogic breathing.
Sit either in a chair with your feet on the floor or in a half lotus position. (Indian style but without the top leg tucked under, just resting on your other knee. ) Pretend there is a string running from your sternum up to the ceiling. Roll your shoulders back and let them drop into natural position so you are sitting up straight, but not tensing anything.
First off: there are two kinds of breath. Chest breathing and diaphragm (belly) breathing. In yogic breathing you want to use both, and in two orders. One, filling your lungs from diaphragm up through your trunk and then through your chest. Then the reverse, from your chest down through the trunk and filling your diaphragm last. Keep in mind that when you breathe with your chest you don't want to raise your shoulders, but expand your ribcage, taking in as much breath as you possibly can till you feel it fill into your throat and your lungs actually press outwards. On a regular basis people dont tend to use the full capacity of their lungs. This results in stale air just hangin' out there and once the oxygen in that air is absorbed by the body it's just carbon dioxide sitting there, stagnant, not helping anyone. This cause headaches, poor digestion, energy blockages and lots of other bad stuff that can easily be prevented. Okay, so you're inhaling, inhaling, inhaling, slowly, by the way, it should take five or six seconds to fill your lungs completely. when you are full hold it for a few seconds before slowly exhaling.
The first few days or even weeks you do this it will probably make you a little light headed. Don't worry, thats you body responding to having a maximum amount of oxygenation being pumped into your blood. It's a good thing. =) Repeat this eight to twelve times, doing half chest->diaphragm and half diaphragm ->chest, whenever you need a little pick me up. It's like your personal anti-depressant and you don't need a prescription!
I do this a few times a day. Usually when I wake up, before I stretch, whenever Im meditating. I find it easier to meditate while doing this type of breathing because I have a really hard time clearing my mind and thinking of nothing, like you're supposed to. Whereas, if I'm concentrating on just breathing, I figure thats pretty close to nothing. I also do it whenver I am stressed, angry, annoyed, sad, need to focus, whatever. It's good anytime, except right before you go to bed. Yogic breathing charges you up and makes you feel alert and awake, even if it does relax you and create a sense of well-being. It gets your blood circulating and that will prevent you from falling asleep.
Good Luck and Happy Breathing!!