Most of previous answers did already point in the correct direction for minimizing air consumption: buoyancy control, perfectly horizontal asset for minimizing friction when moving ahead, minimal and streamlined equipment again for reducing friction, keeping a calm and relaxed state of mind, and control the way you are breathing.
I would add something on the last point: getting full control on how you are breathing is common practice in some disciplines such as Yoga. In my case, the most effective (and safe) way of controlling my breath was to leverage on these three factors:
1) for any respiratory cycle, there is a volume of air which really changes in your lungs, and another volume of air which simply goes up and down your trachea, without even reaching the lungs. This is called the "dead space" of your system, while the volume of air really replaced in the lungs is called the "live space". The sum of the two is your total volume. If you make many short inspirations and expirations, you are using only a fraction of your live space, while instead at every cycle you always deplete entirely the dead space. This means that for getting the same amount of fresh air to your lungs, you are wasting a significant amount of air which simply does not reach them, as it simply goes down and up and is exhaled without giving you oxygen, nor removing CO2. So it is better to make a smaller number of deeper inspirations and expirations (the latter being even more important), trying to maximize the ratio between employed live space and dead space. Most people instead think that using the whole live space will results in more air consumption, and for "saving air" they use a very shallow inspiration/expiration, resulting in very inefficient exhange of gas in your lungs...
2) Your lungs exchange gases more efficiently when fully expanded, as this maximizes the surface of contact between blood and air. So, instead of adopting a respiratory cycle with a perfectly sinusoidal time signature, it is better to modify the "duty cycle", staying more time with lungs full or almost full, and as short time as possible with depleted lungs. In practice this can be accomplished slowing down when the lungs are almost full, and speeding up when they are almost empty. Some people make a true full respiratory pause with lungs full of air, typically around 5s, before exhaling. This practice is discouraged by most instructors, as it can be dangerous for inexperienced divers: staying in apnea increases the risk of a rapid ascent without exhaling, causing pulmonary barothrauma and consequent emboly. But as the diver is more expert and the risk of an uncontrolled ascent without exhaling goes to zero, practicing a short inspiratory pause (never more than 5s and reduced when the work load increases) can reduce greatly air consumption, and improves the overall capability of removing CO2 from lungs, as they are 100% efficient for a larger fraction of the respiratory cycle. Reducing CO2 accumulation is very important for reducing narcosis effects at depth, and for reducing the risk of loosing control of your respiration under heavy work load (as swimming against current).
3) carefully tune the knob of your regulator for giving you exactly the proper amount of air, without wasting any. I use very old Scubapro 108 and 156 second stages, which have a knob giving you great control on the depression needed for making them free-flowing. With the knob all out, the regulator will freeflow as hell, just facing down or swimming, as these regulators, when correctly serviced, can open the flow with a very minimal depression, less than 1cm of water column. So you need to close the knob "just enough" for avoiding free-flowing, which of course causes significant air consumption.
All this said, I never managed to reach the incredibly small air consumption of my wife. Albeit we are almost the same size (she is 1.73, I am 1.75 m, and both weight almost the same), she is using consistently 30% less air than me...
So yes, constitution plays a big role, and is not just matter of size or weight (as in our cases these are almost the same), it is about how she moves in water (she seems a siren, I look like a pig), and particularly on details of the pulmonary system (my wife has a total capacity of 5 liters with 0.8 liters of dead volume, I am around 6 liters, but with around 1.5 liter of dead volume: so the live volume is almost the same, but my dead volume is twice as her, and hence the efficiency of my pulmonary system is much worst).
I would add something on the last point: getting full control on how you are breathing is common practice in some disciplines such as Yoga. In my case, the most effective (and safe) way of controlling my breath was to leverage on these three factors:
1) for any respiratory cycle, there is a volume of air which really changes in your lungs, and another volume of air which simply goes up and down your trachea, without even reaching the lungs. This is called the "dead space" of your system, while the volume of air really replaced in the lungs is called the "live space". The sum of the two is your total volume. If you make many short inspirations and expirations, you are using only a fraction of your live space, while instead at every cycle you always deplete entirely the dead space. This means that for getting the same amount of fresh air to your lungs, you are wasting a significant amount of air which simply does not reach them, as it simply goes down and up and is exhaled without giving you oxygen, nor removing CO2. So it is better to make a smaller number of deeper inspirations and expirations (the latter being even more important), trying to maximize the ratio between employed live space and dead space. Most people instead think that using the whole live space will results in more air consumption, and for "saving air" they use a very shallow inspiration/expiration, resulting in very inefficient exhange of gas in your lungs...
2) Your lungs exchange gases more efficiently when fully expanded, as this maximizes the surface of contact between blood and air. So, instead of adopting a respiratory cycle with a perfectly sinusoidal time signature, it is better to modify the "duty cycle", staying more time with lungs full or almost full, and as short time as possible with depleted lungs. In practice this can be accomplished slowing down when the lungs are almost full, and speeding up when they are almost empty. Some people make a true full respiratory pause with lungs full of air, typically around 5s, before exhaling. This practice is discouraged by most instructors, as it can be dangerous for inexperienced divers: staying in apnea increases the risk of a rapid ascent without exhaling, causing pulmonary barothrauma and consequent emboly. But as the diver is more expert and the risk of an uncontrolled ascent without exhaling goes to zero, practicing a short inspiratory pause (never more than 5s and reduced when the work load increases) can reduce greatly air consumption, and improves the overall capability of removing CO2 from lungs, as they are 100% efficient for a larger fraction of the respiratory cycle. Reducing CO2 accumulation is very important for reducing narcosis effects at depth, and for reducing the risk of loosing control of your respiration under heavy work load (as swimming against current).
3) carefully tune the knob of your regulator for giving you exactly the proper amount of air, without wasting any. I use very old Scubapro 108 and 156 second stages, which have a knob giving you great control on the depression needed for making them free-flowing. With the knob all out, the regulator will freeflow as hell, just facing down or swimming, as these regulators, when correctly serviced, can open the flow with a very minimal depression, less than 1cm of water column. So you need to close the knob "just enough" for avoiding free-flowing, which of course causes significant air consumption.
All this said, I never managed to reach the incredibly small air consumption of my wife. Albeit we are almost the same size (she is 1.73, I am 1.75 m, and both weight almost the same), she is using consistently 30% less air than me...
So yes, constitution plays a big role, and is not just matter of size or weight (as in our cases these are almost the same), it is about how she moves in water (she seems a siren, I look like a pig), and particularly on details of the pulmonary system (my wife has a total capacity of 5 liters with 0.8 liters of dead volume, I am around 6 liters, but with around 1.5 liter of dead volume: so the live volume is almost the same, but my dead volume is twice as her, and hence the efficiency of my pulmonary system is much worst).