Make sure your swing had momentum. Swing with your outside leg and bring it inward as you jump. At the end of your swing around the time when your leg starts bending try extending it for more speed.
Rotate chest and pecs in the direction your leg is swinging to maximize spin.
Raise your arms to give yourself lift and time your jump off the ground so it doesn't look awkward.
When you're in the air it's pretty simple. Lower arms and contract glutes, contracting pecs looks a little more realistic in some cases.
From there you just need to tweak it to make sure you land on your feet.
Swinging through is fairly simple, getting a good setup is rather hard if you don't know how. Lumbar helps so much its unbelivable. Try a basic backflip and then twist slightly to plant on your inside foot. Swing through with the opposite leg, e.t.c.
That's about all I can do without a Toribash client.
Hopefully it helps, I haven't made a replay in a month.