The swing is the basis of all advanced flying trapeze tricks. It allows you to maintain the height of your swing on your own as you start to fly out of lines. Your swing will evolve and improve as you continue to practice it, and there is always something you could do better. A basic swing (called a 'tic toc') differs from an advanced swing in that it does not contain a force out.
As you leave the platform, sweep your legs backwards underneath it, then kick them forwards. For a basic swing, when you arrive at the peak of the swing at the front, push your hips forwards to bring your whole body straight (and lined up with the cables). As you fall away from the peak with your body straight, relax slightly and bring your legs in front of you (a little). This is called a 'hollow'. Then sweep back hard and as you arrive at the platform, bring your legs back in front of you, pull your hips up towards the bar and look over the top. This is the stand or the seven shape (body is like a 7). Now start all over again.
You can find out more about this trick in my books:
Thanks to Fly'n Fit for providing a video for this page.