TL;DR: Probably the most important form. When done properly, breathing is dictated by your cadence ((turnover rate) which, oddly, is driven by "Arm Swing").
This has to do with form because if you hyperventilate, or get a stitch, you're probably not going to have good form (or be able to run relaxed (or run at all for that matter)).
Mouth breathing
There's a dominant school of thought that breathing solely through your mouth - that is in and out, inhaling and exhaling - brings in and releases air at a higher volume than using your nose too. Like never use your nose. Great news for people with stuffy noses. For asthmatics, this is interesting though: some studies show that asthma symptoms can be reduced by breathing in through your nose, not mouth, here for example.
Additionally, an odd benefit of the most recent pandemic (who would have thought there could be a benefit from a pandemic?), is... wearing a mask in cold weather, which provides a warming chamber for cold air and helps sufferers of cold weather (and exercise) induced asthma, to breath through their mouth while pre-warming, and filtering, inhaled air; similarly to nose breathing.
Stomach breathing
Like this:
and almost like this:
Use your stomach (well abdomen). Make your breathing relaxed and deep. Normally, we're shallow, crude human beings, breathers that is, but runningwise, that's probably inefficient. Deep "belly" breathing might be better. When your breath is shallow, you don't take advantage of your total lung capacity. The real trick is to breathe-out quickly and fully. Punch the out-breath. Empty your lungs as fully and quickly as you can, leaving the in-breath to take care of itself. If you don't empty your lungs on the out-breath, your instinct will be to force breathing in, to try and obtain more oxygen. Over filling your lungs on the in-breath stresses your diaphragm (your rib cage can only move so much) and results in a stitch (a similar effect to running wearing a jacket that's too tight).
Oxygen is what your muscles crave, so the more oxygen the better your ability to burn glycogen (brawndo!). Getting rid of CO2 is what your body craves, which makes the fast out-breath so important.
(test: while you're running, put your hand on your stomach (abdomen), to feel if it's rising and falling... like rising and falling as if you were laying down... while running. Oh - just forget it!)
Counting steps to pace your inhale vs. exhale ratio - 3:2
All sorts of science today: To fully oxygenate the muscles and clear the body of CO2, you should inhale for 3 steps and then exhale for 2. Makes for weird dancing. I think System of a Down has a beat that caters to this.
You'll naturally drop to a 2:2 ratio when you're pushing it (or pre-oxygenating, preparing to tackle an uphill section).
Other tips:
- relax your jaw
- unless you're running up hills or at speed, breathe quietly! (I've never managed this one)
- upright posture allows for better lung expansion
- since breathing is synchronized with steps, increasing step turnover rate (cadence) on an uphill (while shortening stride length), increases oxygenation and flushing CO2
- don't over-think it (ignore everything we just wrote)