I've been training for a cross-country cycling tour for years (it'll never happen; I can't get my wife to get on a bike). Anyway, to point is, I ride four days a week. As a new diver, I've not experienced a change in finning styles but that may have to do with what swimming training I've had. For one reason or another I'm capable of "reprogramming" my brain from one activity to another.
As for the breathing, what others have said about being new and needing experience is probably the case. Aside from the cycling, I spend a lot of time lifting weights and participating in high-intensity interval training, so I know my cardiovascular is primed, yet I still suck down more air than I'd like. One of my biggest problems is that, with all my land-based training, I find myself filling my lungs to capacity before emptying them as far as they'll go. (Talk about a buoyancy issue. Yo-yo city.)
I found that this course helped. It walks you through some breathing exercises as well as some guided meditation you can incorporate into your yoga practice. It's still a work in progress for me, but I can already see an improvement.
+1 on this. While not everyone who rides has had this experience, which is clear by this thread, some of us have. I needed to drop the habit that I think came from yoga and riding to fill my lungs and empty them with each breath. Once I was able to manage that, my buoyancy and air consumption improved greatly. What it took was for me to be told by an instructor that my breathing underwater should basically be the same as my breathing above water.
All the other advice about relaxing and using less effort is spot on, too. But none of that happened for me before I adjusted my breathing first. Good luck!