RE: How do you hit a running deer?
First, you're not ready, so don't attempt this, yet anyway.
You need to practice as others have stated. Here is one way to do it;
Rolling wheel - get an old tire, one that is pretty tough, like a truck tire. Carrige bolt some plywood on the inside and staple targets to it. Have a friend roll it down a hill that has some bumps. The bumps will make the tire bounce and simulate a deer jumping through the woods. Most who understand this way of shooting agree that the shot should be taken while the animal is in the air, since it is "committed". Meaning that it cannot stop, change directions, or speed as they can while on the ground. But this is a very challenging shot. The single biggest reason for its challenge is that you can’t take advantage of the accuracy associated with being surprised by the shot like you would if you were shooting at a still target. You will have to pull the trigger knowing that the gun is going to fire and you will flinch. This applies to timing the shot, meaning finding an opening and shooting though it when the deer is passing through or with leading, meaning keeping the gun on or just ahead of the animal while it is moving.
So, you'll also need to get to know your flinch. You can do this by standing while aiming your weapon. Have a friend command when to shoot. As soon as the command is given, you need to shoot. Since the danger that is causing you to flinch is understood, always in the same spot (five inches from your face) and expected, your flinch should be somewhat consistent. Once you know how you flinch, you'll be better at making these shots and you should use this info while practicing. I have found during my practicing, that I am the most accurate with the single bead on the end of a smooth bore shotgun barrel. Next would be a rifle with iron sights and lastly the scope. Further, I would recommend using slugs rather than buck shot. Some will disagree, but there are many advantages to slugs. They are distance, energy at any given distance and the biggest one for this topic would be either hitting the animal or having a clean miss. If you hit an animal with just a few buck shot pellets, they will most likely live for a while or recover. You may not even think that you’ve hit them, and only track them for a short distance if at all. I don’t think this is a fair way to treat these animals. A slug normally leaves no question whether there was a hit or not. The animal will either collapse right there on the spot, run only a short distance, or if the hit wasn’t great, there will still be a great blood trail.
For those of you who disagree, please go study the ballistic coefficient of buck shot pellets before arguing. It does have some very poor numbers.
On another note, I would first recommend not jumping the deer. This is your best case for a good clean shot. If you are continually jumping deer and you are using a scoped weapon, it sounds to me like you were in shooting range and didn’t see the animal was near by. You should be using binoculars, moving very slowly and scanning the entire area before proceeding. Shooting at a moving animal to me would be the last choice, only after all else had failed. Further, since I do not require the meat from these animals for me to survive, I would and have elected to pass on these shots.
Good luck,
KP