Breathing for me is simply a means to an end, so to speak. Sure, you have certainly got to slow it down enough to break a clean shot, and you can not do that while continuing to breathe, but slowing my heart rate is of ultimate importance to me.
I drop down and get to position without wasting time, but not getting worked up in the process. When I know I've got to make a shot here in seconds, mentally I calm myself "back" down while I'm preparing for the shot, kind of like I'm getting ready for a nap type deal.
Got my clicks on and looking through the scope at my target, which I never take my eye off of for nothing. 30 seconds, 2 minutes, just don't seem to bother me keeping my eye in it for some reason. But I set my crosshairs low left and watch for them to top out on my target on total exhale, adjust the butt lower if POA is still too low. Once I've got that right I'm pretty much dealing with heart beat on the exhale. This is why I probably like to hold lighter than some guys, heartbeat seems to have less POA deflection and longer dwell time. Wait for the predominant wind condition I'm dialed for, three or four heartbeats and the bullet's on its way, or I breathe again two or three times and take it from the top again.
Being concious of my heart rate the whole time is what I focus on, so breathing correctly and slowing down becomes 2nd nature so the shot's placed well. Otherwise it's a rush to waste a shot, or a waste at a good chance for a shot because you're excessive heart rate has the crosshairs bouncing 10 MOA accross your FOV in a fevered pitch that you can never shoot accurately with.
Sometimes if my rear rest is not so good it works better to get set up high right on exhale, then take a good breath, hold, then fire. It must have something to do with what Ryan was describing, I'm sure.