I purposely breathe more deeply underwater. I fill my lungs from bottom to top and exhale slowly from top to bottom with a pause at each interval. Consciously breathing in this fashion quickly became habitual. This “technique” improved my air consumption, but you have to find what works best for you.
This is how I was trained, back in the seventies, mostly using the ARO (oxygen rebreather), but also with air scuba.
There are three factors to evaluate for optimizing breathing:
1) proper gas exchange (eliminating CO2, mostly, as Oxygen is already too abundant)
2) reducing the effort for breathing
3) reducing SAC
The order of importance is as above, 1) is of utmost importance, reducing SAC is quite less important.
In the fifties-sixties, here in Italy, it was much more common to use oxygen rebreathers than air cylinders, hence learning the proper breathing technique, for avoiding CO2 accumulation, was absolutely important.
Breathing normally is absolutely NOT effective for avoiding CO2 retention, as normal breathing is very short, the vented volume for each breath ranges between 0.5 liters to 1 liter maximum. Considering the dead spaces in your pulmonary system and inside the regulator, it means that up to half of the vented volume never reaches your lungs. So you make a lot of effort (and consume a lot of air) obtaining bad gas exchange.
It is much better to employ always almost entirely your vital capacity, which can be as large as 6 liters (it is 5.2 liters for me). Of course, the number of complete ventilations per minutes must be reduced. At the end you will vent less liters per minute, but almost 90% of it will reach your lungs, giving you much better capability of eliminating CO2. This is the most important thing for tech and deep diving.
Let's go to the second point.
If you look at the chart of pressure-volume of a modern regulator, you will see that for initiating the inspiration you need to provide some depression (around 0.7-1 inch of water), but then the venturi effect reduces this to almost zero, or in some regs, with a lot of venturi effect, it even goes to positive pressure "inflating" your lungs. At the end of the inspiration, you again need to exert some positive pressure for closing the inlet valve and opening the exhaust valve, then again the venturi effect reduces the effort during the expiration.
This means that every cycle you get two strong peaks of negative and positive pressure that you have to provide with your muscles, followed by a phase in which the reg is less demanding. So if the cycles are very long and a few each minute, you spend much less time exerting these larger pressures, and you make much less respiratory effort. Instead if your breathing is "normal", you make a lot of short cycles per minute, and the regulator never goes in the low-effort state, as you immediately invert the flow.
And finally, reducing the SAC. After having already got a fully controlled breathing, employing always the whole vital capacity, and with very slow rate, then for improving SAC the final trick is to add some short inspiratory pause.
This is what many instructors advise against, as they fear the risk of pulmonary embolism if the diver goes up without exhaling. This is a serious risk, so only divers with enough skills and experience for being 100% safe against this can risk experimenting with the inspiratory pause. One could think that interrupting breathing could work against requisite 1), causing CO2 retention. In reality, a proper inspiratory pause does not only improves SAC, but also helps eliminating CO2. This is because the rate of gas exchange in your lung is proportional to two factors, the pressure difference between CO2 in the blood and in the gas mixture trapped in the lungs, and the surface of contact between blood and gas.
Such a surface is maximised when the lungs are completely full, hence, for a certain period, this overcompensates the fact that, while time is passing, the pressure difference reduces. Of course there is an optimal duration of the inspiratory pause, which is inversely proportional to the CO2 production (hence to the muscular effort being done).
In some type of diving, for example in a pass at Maldives, the diver is completely steady, looking at fish (sharks, eagles, manta rays) passing above him through the pass. The water is warm (usually no suit is needed), the effort is minimal, and the inspiratory pause can be up to 10s. When swimming, particularly if attempting to swim fast with short, hard fins, and using inefficient kicking (for example bicycle or frog kicking) the muscular effort is high, and the inspiratory pause cannot be longer than 1s.
I would say that in average conditions a pause around 4-5 s should be OK, but each one has to evaluate this according to his metabolism, muscular activity and kicking capability. Forcing it too long causes CO2 retention, which is something really bad. Remember, learning a proper controlled breathing method is mainly aimed exactly to avoid CO2 retention! A pause of proper length eliminates more CO2 than without any pause, as your lungs are fully extended, exchanging gas at maximum rate, during such a pause. But beyond a certain duration this is not true anymore, and is better to start exhaling, for expelling the CO2 which is now trapped inside the gas mixture in your lungs.
As you cannot swallow a CO2 meter for checking what is happening inside your lungs, you have to learn how to adapt yourself the length of inspiratory pause.
All that said, I did usually never teach all this to my students, and I just ask them to breath continuously, simply more slowly than when on the ground. This is much more safe for the instructor... And when teaching in a resort, all the training and certification must be accomplished in a few days and in just 4-5 dives. So there is really no time enough for learning proper breathing. It takes several months, perhaps years...