The turn-vault is used to get on the other side of a rail, wall or other such obstacle that has a considerable drop on the other side. It can also be useful when you are unsure of the landing surface on the other side of a vault.
Start with your body 2-3 feet away from the rail. Place your left hand on the rail with the palm facing up. Place your right hand on the rail with your palm facing down.
Start out by jumping up and over the rail while keeping your left hand on it. As you are going upwards, lift your right hand off of the rail and rotate 180 degrees around your left arm, so you'll be facing the opposite direction of what you started.
With your arms nearly at full extension above the rail, place your right hand back onto the rail this time on the other side of your left hand. Keep your eyes on the rail the entire time.
At this point you'll be coming down and want to be concentrating on your foot placement. As you come down with both of your hands on the rail, try to land with both of your feet against the wall and absorb into a crouch. So your rear will be about parallel with your feet. Having your legs tucked against your body will help you maintain better control.
Once you land the turn-vault and absorb into a crouch, you'll be ready for the drop. Push off with your feet while at the same time letting go with your hands, and turning slightly.
As you begin to turn and let go, spot your landing. The end goal is to let go and turn 180 degrees so you can land and continue your run.
Land in a crouch or roll, and continue on your way.