To me, the easiest way to do it when you begin is not quite the same as the one you'll find easiest when you start mastering the technique, so don't take my advice as universally true, they're just what I think you should have in mind when beginning. What really fits you best, you'll find by yourself when you master this basic method well enough...
DO NOT shoot your legs upwards (very common beginner mistake). Bring them high when you coil your body in the first place, but that's it: don't try to get them any higher during the move. Shoot them strictly FORWARD.
Don't pull your feet back to soon (even more common). It's very unlikely that you shall fall on your behind, your body should pull them back for you soon enough in a natural reflex, willy nolly (just like your hands will automaticallly spring in position if you fall forward. Natural reflex, very difficult to struggle against). So don't even bother to think about doing it, it will come by itself; on the contrary try to let your legs fly in the air for as long as possible. A good idea is to practice on a very soft surface like your bed, where any fear of falling on your back will be removed, allowing you to find the proper way without any "parasite" body reactions.
Use this mental image: when you coil your body, picture yourself fitting in a very tight box. Then when you explode, burst the box open by:
breaking the front (NOT top) panel with your feet,
breaking the back (NOT bottom) panel with your hands,
breaking the top panel with your groin. (this pelvic thrust is very important for the technique to work)
All these are exploding rapid movements, and they all take place at the same time. Then don't forget to briefly contract your six-pack to get your torso back upright.
Hope it helps!