deep breathing

A component of relaxation practice. Under stress, most people breathe shallowly and irregularly. Conscious focus on deep, regular breathing helps bring awareness to points of tension in the body and gives the mind a break from worrying over the challenges of the moment. Deep breathing is also a good practice if you are quitting smoking: every time you have an urge to light a cigarette, step back from what you are doing, breathe deeply, and maybe stretch a little, for a couple of minutes.

Deep breathing, or breathing exercizes are one of the most important parts of a yoga practice. But anyone can benefit from breathing exercies. To properly execute a yogic breath, one must draw out the breath. If being done along with a yoga posture or asana, you should try to match the time it takes for you to move into the posture with the time it takes to inhale or exhale. For example, if you are raising your arms above your head while you inhale, you should move your arms slowly and breath in the whole time you are moving your arms.
A very simple breathing exercize that can be done anywhere (I do them at my desk at work all the time) is to inhale into your belly. Your belly should rise when you inhale, not your chest. Hold the breath for a beat, and then exhale, making the exhale slightly longer than the inhale. Try to exhale all the air out of your lungs. Do this several times in a row.
When using breath with yoga, one thing is important to remember. Inhaling is considered an opening activity, so inhale with opening movements, like lifting your arms above your head or coming out of a forward bend. Conversely, Exhaling is considered a closing activity, so exhale with closing movements, such as bringing your arms down by your side, or going into a forward bend.
In yoga breathing is considered pranayama.

I would also like the preach the benefits of deep breathing, only from a different perspective.

As a person with severe asthma et al, deep breathing has saved me from many a trip to the hospital, or at least long nights of albuterol induced insomnia. Especially when i'm crying (imagine that, i'm also a guy), or hyperventilating. It helps if you have a person there (or on the phone) to coach you through it, bascially just counting your breathing off for you, or breathing loud enough to be heard over your own gasps. It gets very hard to focus on much of anything when the fullest breath you can get is about an 1/4-1/8 of normal. Panic is a keyword. It feels like your mind is numb, and about to pass out. But either way, it helps stop the randomness of your breathing, and stabilize your mind

As a practitioner of kung fu, it truly saddens me that the importance of the breath is neglected during most discussions of martial arts that I encounter. Deep breathing as mentioned here is the first breathing exercise we are taught at my dojo.

Even if one is not a practitioner of the martial arts, learning to breathe naturally from the hara can be beneficial in many ways. To foster the proper development of deep breathing our sifu recommends this practice once a day:

First off, lie on your back. Place one hand on the chest and the other hand on the stomach. As you breathe, make a conscious effort to raise the stomach hand with the inhalation and let it fall during the exhalation. The chest hand should remain stationary.

The goal is to develop this breathing pattern until it happens subconsciously. I find that when I practice this exercise right before bed it relaxes me so much I have no difficulties in falling asleep.