This is the way I did it, not that I was ever trained, but I could throw the ball from the sidelines across the width of the field in my day. Most important on the set up is your grip on the ball, you want the spacing to be closer than a normal throw in so you'll be able to support your body during the handspring, a few inches between your thumbs at most. After that it's simply a matter of going for it and doing the handspring and completing the throw. Don't hesitate once you begin to go.
It will help to practice without a ball first. Don't use more that four or five steps for your run up, but you'll want to get some speed up and you'll want reps using the same amount of steps each time kind of like a placekicker. Also you'll have to practice with different release points to find one that gives you the most distance.