Cigar Mouth: For a streamlined breathing pattern, attempt to take as little of the head as possible out of the water when breathing. The best way to think about this is "smoking a cigar" when you inhale, meaning, for you healthy, non-smoking triathletes, that the breath only comes from the outside corner of the mouth while the inside corner of the mouth is under the water. As you learn this breathing method, you may end up swallowing a bit of water, but long term practice will result in more efficient swimming.
Swallowing water? That's an understatement! I'll keep plugging away at this, but I feel like I'm starting learn to breath water! There's actually several drills that the breathing can be practiced nicely with. The shark fin is good for practicing this. You swim on your side with one arm extended in front of you, head down, and slowly pull drag your hand/elbow along your side with your elbow straight up in the air like a shark. You can either just keep doing this on one side (and practice your breathing with this), or switch and do the other side. All in all, its a good time to focus on smoking a cigar too.