You can learn this trick once you're confident hooping around the waist and doing the Lasso (see Lesson #4).
The Corkscrew can be learnt in two parts. First moving the hoop from your waist up to the Lasso, and second moving the hoop from the Lasso back down to your waist.
I will explain this trick for those who hula hoop to their left (anti-clockwise), so if you hula hoop to the right reverse the hand and turning instructions.
Start with the hoop spinning around your waist to the left. Place your right hand on the centre/small of your back and let the hoop move over it. Leaving your hand in place, start turning on the spot to your left. Then, when you feel the hoop move over your right hand grasp it and, while continuing to turn to your left and leading with the elbow, lift the hoop above your head so that you are now doing the Lasso.
Then, while doing the Lasso with the hoop in your right hand, start turning on the spot to your left. While continuing to turn, lower the hoop back down over your head to your waist and give it a big push.
This trick is hard to get your head around at first...but practice makes perfect!