It's a nit, but as long as you're breathing, Mike, you're not breathing incorrectly in my book. I tell students the same thing. That said, there are definitely ways to improve your breathing in order to a) maintain neutral buoyancy and b) extend the life of your gas supply and therefore bottom time.
Some good points made by previous posters. Scuba's exciting, so it's natural to be amped up, especially as a beginning diver. What you'll start to realize is that you really want to slow down. Way down. Then slow down some more. Not just your breathing, but everything: moving slowly and deliberately through the water will reduce your need for oxygen, increasing your bottom time. I took up bikram yoga after starting diving and found it helped my gas usage immensely, because I learned how to control my breathing and how that impacts everything else I was doing, to include diving. YMMV but I recommend it to most student divers I work with. (NB, any style of yoga should do the trick.)
Some of the other posters have correctly pointed out that breathing too deep will affect your position in the water column, and they're spot on. It's why exhaling is as much a part of descent as deflating your BCD - the air space in your lungs is an important factor and if you're neutrally buoyant, exhaling should cause you to descend and inhaling should cause you to ascend, everything else being equal. Controlling your position through breath I find is mostly a feel thing - there will be a moment in your training where it just clicks and you're able to do it. (That's what happened to me.)
I'm hoping some more experienced pros can offer a better, more teachable way to explain the relationship between breathing and neutral buoyancy as I find I struggle to put it in different t ms when the students don't intellectually pick it up from the above explanation...