Breathing is one of the cornerstone principles of the Russian Martial Art, Systema. This is a very indepth subject and touches on the relms of health as well as combat efficiency.
I have some exercises and drills relating to breathing on my site
http://www.russianmartialart.org.uk, but I can give you some of our ideas on the subject here.
First you should breath in through the nose and out through the mouth. The mouth should be 'O' shaped on the out breath. The more intense the physical activity you are carrying out the sharper your out breath should be. Concentrate on the out breath and not the in breath. The body as an organism will regulate the amount of breath you need to take in. Doing this will control hyperventilation.
When carrying out any movement your breath should proceed your movement slightly and last throughout the movement being carried out. The way we practice this is to use breathing during exercises such as squats, pressups and leg raises. Using pressups as an example start breathing in and continue the breath smoothley throughout the press to the raised position. Breath out continuely as you sink to the bottom position of the pressup. This exercise can be reversed with the breath out being used for the movement from the floor to the raised position.
Another thing to learn is to regulate your breathing to the amount of air you need for the movement. There are lots of exercises for this. This include slowing the pressups so that each one takes a count longer than the one before. Make the in and out breath last the length of each movement.
To learn to breath through physically difficult exercises try doing slow pressups and squats. The breathing should get sharper and and more frequent as the tension increases. Try making the pressup last 1 minute.
Another thing to take into account is the bodies natural reaction to fear where it holds it's breath. This causes more fear because the body starts to panic at the lack of oxygen. A good exercise to get your body use to this is to do 20 pressups. During the first five you make an in breath last the time taken to do these press ups. You then hold your breath for 5 pressups. You then make your out breath last 5 more pressups and the final five you do on empty lungs. When this becomes easy try going twice around without a break in the two sets of 20.
One of the tips I got from a Russian Special Forces Soldier was that if you feel frightened before a fight take a step back as you breath in then exhale as you step forward and go to work.
There is plenty more to this including breathing to relax during stressful situations, breathing for health and using breathing to take strikes on the body.
Paul Genge