I played a bit with slings too. I used a patch of leather for holding the projectile and made a sling around the wrist. A small patch of leather on the lose end makes it easier to hold and release smoothly. For the release you just ease pressure and let the momentum of the stone pull the lose end out of your hand. It should take 2 or 3 circles to accelerate and a straight line motion of the hand for the shot (just like throwing a ball at the target). Bear in mind that you aim with your feet. The shot should be made with the same motion every time. When you´re looking at the target and you miss to one side, you should turn a little (move your feet for that). Don´t try to compensate with a different arm movement. With a little practice you should be able to predict the proper stance.