With a broadside, get the cross hairs on the front of his shoulder, and swing with the animal, and keep swinging as you fire the shot. Amount of lead varies with the distance to the target. If he's less than fifty yards away, I would only lead by inches, but you must keep the swing moving as you fire. Follow through.
For a shot angling away, which is common, you don't need as much lead. You have to really focus on AIMING, not just throwing lead. Take the time to actually get on the animal. Gain experience by doing it. Running rabbits are perfect, as previously mentioned.
Good luck, let us know how it goes.