I used to follow a recommendation that you see quite frequently around here: take slow, deep breaths. This works and makes for a comfortable dive, however at least in my case, it also results in quite a high air consumption rate. I don't know if I have larger lungs than other people, but that's what I got with that technique. Another side effect is that your buoyancy swings are quite large.
Then I noticed that under normal circumstances, I don't really breathe like that, and I'm not sure if anybody does. Like right now, sitting at the PC, I don't normally breathe in fully, and I also don't really fully exhale. In other words, I'm actually breathing relatively shallow, with my lungs more on the empty side on average. It has been my goal on all recent dives to achieve this same breathing pattern underwater, however without forcing myself to breathe shallow (because that can be dangerous).
I'm not fully there yet, but getting close. Air consumption is down, even though I'm now probably taking more breaths per minute than before. This also allowed me to drop some weights, which in turn means I have to fiddle less with my BCD. I get into the most natural breathing pattern when I get slightly distracted, like when concentrating on some interesting critter and trying to get some nice pictures or video of it. I totally forget about breathing and what happens is that I suddenly start sinking, when before I was neutral.
This also leaves a lot of "head room" in your lungs that you can use to adjust your depth or (temporarily) buoyancy. I think that this is what "breathe normally" from every dive course is all about. But in order to do that, you first have to get used to the feeling of sucking compressed air out of a hose, under water.