What you're looking for is a slow, rhythmic, even inhalation and exhalation. We always say, "Take slow, deep breaths," but I've discovered while working with students in the pool that, if you're a big guy and you do this, the buoyancy swings from very full lungs can be unnerving at best! What you want to do is take very slightly larger than usual breaths, and exhale a little more than you do at the surface, but not a lot -- and take your time doing this.
But as has already been said, new divers look at their high gas consumption and immediately assume it's because they don't breathe properly. Some of it is -- the nervousness of being new tends to cause people to take shallow, quick breaths, which is very wasteful of gas. But a lot of the consumption issues are because new divers are inefficient divers, and efficiency is where it's at for maximizing bottom time on a given amount of gas.
So how do you become efficient? First off, get properly weighted. Being overweighted leads to difficulties with buoyancy control and a lot of yo-yoing, which causes stress (faster breathing) and wastes gas in inflating and deflating the BC.
Get horizontal. This may involve moving some of your weight around -- usually up onto your back in some fashion, using trim pockets if your BC has them, or camband weight pouches, or tank weights. If you are feet down, as many new divers are, then each time you kick, you drive yourself upwards. In order to avoid ascending, you have to keep yourself negative. So each kick wastes a certain amount of energy that results in no net displacement at all! Being horizontal means that all your kicking energy MOVES you where you want to go.
Don't swim with your hands. Hands move very little water; they aren't an efficient way to move yourself around. New divers often make extensive use of their hands, because they feel out of balance. Learn to correct your balance with your fins. (Gear that is properly adjusted helps a lot with this, because keeping the tank in the center of your back makes balancing much easier.)
Move slowly. This is sometimes difficult for new divers, because the slower you move, the better your balance has to be. You can make up for deviations from neutral buoyancy if you swim; when you stop, you sink or rise. Fix the buoyancy, so you don't need to swim constantly. If you are interested in marine life, you will see far more of it if you go slowly. Camouflage is one of the biggest survival strategies in the sea, and it's easy to swim right past some of the most interesting animals, if you're moving too fast.
And finally, go diving a lot. It takes most people some time to feel solid enough to really relax in the water, and relaxation is the final key to good gas consumption.
As you can see, changing your breathing wasn't even mentioned in the list, because it generally fixes itself as you fix the other things.
