I must've had to say that about a thousand times.
It all boiled down to practice. Practice, practice, practice. More importantly, practice how you will be shooting in the field. There is no bench. Practice prone, sitting, kneeling, with shooting sticks, and offhand.
When I am shooting my .308 precision rifle and I have to go to my target, I walk very slowly, trying to not get my heart rate elevated. However, to practice for shooting a deer, I would say jog out there, and jog back. Shoot kneeling, or some other equally uncomfortable position, and learn to get very good at that. Learn to control your breathing, which will slow your heart rate, and learn to shoot between heartbeats.
Also, a deer is not a stationary steel plate standing out there waiting to be hit. It will move. So, take all the stuff above, and cram it into a pattern or rhythm of "1,2,BAM", which starts as soon as the deer presents a good shot and you have your crosshairs on it. Learning to get a GOOD, ACCURATE shot off QUICK will hopefully avoid watching the thing run away.