I was wondering what everyone's slinging style is.  Personally mine is overhand slightly tilted, much like a baseball pitcher's throwing style, with no wind-up....works good for short rannges.

I've tried many, many styles, and have found out two that I beleive are the best (at least for me):

If the target is near, like 20m (65') away, I use the overhand throw. But not with the style shown here in the articles. I start with my hand slightly in front of me, but still of course enough on the sides so the sling won't hit me. Then I quickly swing the sling (not the hand, at least not much) backwards in an arc, and release the projectile at the right moment. I've found this to be the most powerful 'target hitting' style on close ranges. The only minus is that it's easy to swing the sling in a wrong way, resulting in a sore hand next day.

On long ranges I use the greek underhand throw, but still not quite as shown here in the articles. At the end of the swing, I use all (or most of) my strength to simply lift the sling straight upwards. It increases the speed of the projectile tremendously, although it makes it a bit harder to control the vertical direction of the projectile. And that's the reason I don't use it on short ranges.

I use a underhanded fast softball pitch. I figure if women can throw a huge softball very fast with this method, it will work for me too.

I had been using an overhand throw with a sling measuring from my elbow to my ankle.  After playing around with Nwmanitou's figure 8 toss, I've switched to a shorter sling and that style for close-up target practice (10-30 yards -- I still can't hit anything to save my life, but I'm missing more consistently) and an underhand whip for distance.  After a little practice, I found that the underhand whip with a shorter sling was getting the same distance as my overhand with the longer sling.  My next experiments will be with a longer sling (again) and underhand-sidearm-diagonal toss.