Welcome, indeed! Weapons of an unusual nature, eh? That's us, for sure.
Here is another link to
detailed instructions
for making a sling from any sort of cord, and tape (the author uses medical tape, but duct tape also works very well).
And here are a couple of
techniques
to start off with, with videos so you can see how it is done.
Or if you have ever played baseball, you can try this technique: Stand like you were going to throw the ball, with the sling in your throwing hand (your right hand, I assume). Spin the sling slowly overhead, so that the sling passes in front of you from right to left (reverse this if you are left-handed). Get a feel for where the sling pouch is, and when it is directly behind your head, whip your arm forward just as if you were throwing a ball, and release the sling cord when you would let go of the ball. It is amazing, especially if your sling reaches from your hand to the middle of your chest. The timing seems to just work out so that the ball will go pretty much toward where you are aiming.
Please use tennis balls, when you are learning. Even though David Taylor's techniques, and the technique I described, work well, mistakes happen when you are learning a new skill. Tennis balls don't hurt as much when you drop one on your own head. I speak from experience! If it had been a stone, I would not BE here to speak...