The overhand throw. (see 2nd video for demo)
This is the safest and easiest sling. With your trigger hand close to your body, hold the loaded pouch out in front of you. Point the shoulder of your non-slinging arm toward your target. Drop the pouch and swing your slinging arm with the fall of the pouch to accelerate in a circle. As you approach the top of the arch, lengthen your arm out all the way and release the trigger at the top of the arch or just before.
DON'T SWING THE SLING IN A BUNCH OF CIRCLES! You can't get the pouch going much faster than you can on the first pass, plus it increases your chances of hitting something, or someone, you did not intend to hit, including yourself. Admittedly it looks cool, but that's about it's only usefulness.
Get your sling on...