Breathing techniques and practices are a vital part of both yoga and qigong practices. The breath is identified or associated in these popular mind-body practices with "energy" or "life force" or "Force" or "Élan vital" as elaborated in descriptions of the concepts of "Chi (Qi)" in Chinese and "Prana" in Sanskrit. Air and Breath have since ancient times been essential features of both naturalistic and metaphysical explanations of living processes on earth. Unquestionably, breathing and physiological respiration and moving oxygen through our blood are all essential to maintaining life. Yoga and Qigong (Neigong) claim that their special breathing practices improve vitality, strengthen the body, improve immune response, calm a troubled mind, and possibly increase longevity.Yoga has many unusual breathing practices. Breath of Fire - rapid short exhales. Alternate nostril breathing - long slow breaths in through one nostril only. Reverse abdominal breathing - tighten the abdominals on the inhale, relax the abdominals on the exhale. Exhaling through the mouth with the throat constricted. Breath retention for long periods. Humming like a bee while exhaling. All of these practices are called "Pranayama" and are taught in many yoga classes.
Qigong uses breath control and coordination with movements to increase power, circulate and store energy in channels and reservoirs the mind-body realms, quiet the mind, and improve and expand the spirit-mind. The main breathing technique encouraged is natural abdominal breathing: relax the abdomen on the inhale, slightly tighten the abdomen on the exhale, and don't hold or exaggerate the breathing cycle. The more unusual and extreme techniques for breath control found in the Raja, Kundalini and Hatha Yogas from India are not found in Chinese Qigong. More emphasis is placed in Qigong and Tai Chi on gently coordinating breathing with specific movements, and using one's mind to coordinate and direct the use of the inner life force energy (Qi) for health, well being and enlightenment. Some contemporary Qigong teachers, of course, have borrowed techniques from modern Iyengar Hatha Yoga and use these in their Qigong (Chi Kung) classes.
Overall, for the purposes of maintaining good health, I recommend breathing through the nose and out through the nose. Do not smoke tobacco or other drugs, and avoid polluted air. I wear a mask when working in dusty, smoky, or otherwise polluted air. I also cover my mouth and nose when breathing in very cold weather. Get prompt medical advice and support for serious respiratory problems. Maintain appropriate cardio-vascular conditioning with aerobic activities like brisk long walks. Just breathe naturally as needed depending on one's exertion levels.
As for using breathing techniques or mantras or chants to meditate and attain "insight" or "enlightenment" I would recommend instead the daily reading of challenging and wise books and good conversations with intelligent and decent people. Certainly, if you need to calm the body and quiet the mind because you are upset then then please sit quietly, close your eyes, breathe slowly and listen to some soothing music. I find little benefit, for my mind or body, in using the unusual esoteric breathing practices of Hatha Yoga. Likewise, I benefit more in many ways from walking for four miles rather than by staying still in seated meditation for 1.5 hours. These are just personal preferences - just one fellow's opinions.
The Taoist classic, the Tao Te Ching, by Lao Tzu, circa 500 BCE, has some verses that indicate that excessive emphasis upon breathing techniques and methods is not recommended. The Taoist emphasis is more often placed on being natural, softening, being more pliable and flowing like water, not straining, and not interfering. In particular, let's look a Chapter 55:
"To increase life means inviting evil.
To control the vital breath with the mind means rigidity.
When things have matured they age.
Such control is contrary to the Way.
What is contrary to the Way will soon end."
- Translated by Jan J. L. Duyvendak, 1954, Chapter 55
"It is inauspicious to try to improve on life,
And harmful to regulate breathing by conscious control.
To strive for too much results in exhaustion.
These actions are contrary to Tao.
And what is contrary to Tao soon comes to an early end."
- Translated by Keith Seddon, Chapter 55
"All devices for inflaming life, and increasing the vital Breath, by mental effort are evil and factitious.
Things become strong, then age.
This is in discord with the Tao, and what is not at one with the Tao soon cometh to an end."
- Translated by Aleister Crowley, 1918, Chapter 55
"To help life along is to bring ill portend;
To use mind (hsin) to direct the life breath (ch'i) is called the strong (ch'iang).
When things are full-grown they become old,
It is called not following the Way (Tao).
Not following the Way one dies early."
- Translated by Ellen Marie Chen, 2000, Chapter 55
"Increase of life is blessedness, they say,
They call the heart-directed spirit strength,
But these things reach their fullest growth, at length,
And plunge to swift decay;
We call all this contrary to the Tao,
Whatever is contrary to the Tao
Soon will pass away."
- Translated by Isaac Winter Heysinger, 1903, Chapter 55
"Trying to extend one's life-span is dangerous and unnatural.
To manipulate one's energy with the mind is a powerful thing
But whoever possesses such strength invariably grows old and withers.
This is not the way of the Tao.
All those who do not follow the Tao will come to an early end."
- Translated by John R. Mabry, Chapter 55
"To speed the growth of life is an omen of disaster;
to control the breath by will-power is to overstrain it;
to grow too much is to decay.
All this is against the Dao
and whatever is against the Dao soon dies."
- Translated by Tom Chilcott, 2005, Chapter 55
"Fuelling the vital spirits is called disastrous.
Mind impelling the breath is called violence.
The creature that ignores what exists from of old
Is described as going against the Way.
What goes against the Way
Will come to a swift end."
- Translated by A. S. Kline, Chapter 55
The Chinese characters for this passage are:
yi shêng yüeh hsiang.
hsin shih ch'i yüeh ch'iang.
wu chuang tsê lao.
wei chih pu tao.
pu tao tsao yi.
心 使 氣
hsin shih ch'i
heart/mind directing/controlling vital energy/breath