Getting there...not so easy.
As usual, it's getting there that's the hard part, but not undoable. Face your non-slinging shoulder towards the target, let your sling hang straight from your slinging arm behind you. Take one slow wind-up around your head just to get the sling moving, take a second turn, still slowly around your head to flatten the plane of rotation so that it's parallel (lined-up) with the ground, on the third turn accelerate and release. In this video, I'm swinging at least twice most times which is all that's needed, but I've found that the extra swing produces more power and better accuracy... also notice the way I step into the line of fire upon release, I highly recommend this as it vastly improves distance in particular...