There are well-understood methods for breathing in the world of classical woodwind and in opera singing that apply equally well to playing shakuhachi. The more breath your body can accommodate at any given moment, the more fuel you have to exert control over your instrument. Perhaps counter-intuitively though, you don’t need an unusual breathing capacity to play shakuhachi. You don’t need to be a runner, you don’t need to have an especially developed aerobic function. What you DO need is to be able to take a full breath, and then use that breath as efficiently as possible in the sound-making (and often long) expulsion.
Unless you have been trained to do otherwise, it’s likely you will be breathing in and out rather shallowly in your daily life...not utilizing all of the lung capacity available to you in either breath direction. The expulsion in particular is often very short. With a little attention, your breath intake can be dramatically increased, as can the length of your expulsion.
Breathing begins and ends at the 'hara', the abdominal muscle wall area around the belly button. Breathe in by distending the abdominal wall gently outwards and avoiding a 'shoulder shrug' at the end of the inhalation.
The exhalation of the breathe through the flute can be visualized as a soft wind sourced deep inside your lower abdomen. All the throat, mouth and lung cavities should be open and free of muscle tension, as the air leaves the body. You will notice that, at the end of the exhalation, you will feel a slight muscle contraction around the belly button.
Whether you breathe through your mouth, nose, or a combination of both, is less important than what you do with your embouchure during the intake. It’s a good idea to deconstruct your embouchure on the intake, that is, let it go completely relaxed during the intake, before shaping the lips once again to blow the next note. This has several advantages . Making and re-making your embouchure gives the muscles around the mouth a chance to relax, and you also get the chance to remake your embouchure as a higher functioning device, several times in one phrase.