I have never had the expectation that I would ever get more than one shot. I have watched too many animals run knowing full well that the situation and geometry conspired to make it a "No Shot" scenario. For this reason I have this mnemonic that I run thru routinely while hunting... "Slow is smooth, smooth is fast".
To make this happen, as blasted_sabre described one needs to "Train the way you hunt". In the military they say "Train the way you fight" and it is the basis for all performanced based training. Get your tool of choice sighted in properly. Then practise, practise and then do it again.
This does not mean you have to be shooting real bullets. This activity can be done dry fire. There is no harm to dry firing centre-fire rifles so go to it. If you still doubt me simply load in a spent case and let the firing pin strike the spent primer. This will allow you to go slowly through the mechanics of shooting (even in your garage) without scaring the neighbours.
Bring the rifle up to your cheek, sight target, breath out and stop breathing... squeeze completely on the trigger and hold it in the most rearward position for a half second.
There is a great series of videos on YourTube taught and narrated by Ryan Cleckner of the NSSA (He is a former Captain in the US Army Rangers, sniper team lead and good narrator).
You can read about his creds in this link
http://en.wikipedia.org/wiki/Ryan_Cleckner