The Trouble with Double-Unders (by Jon Gilson of Again Faster)
Jumping Too Early:
Time your jump so it happens just before the rope hits your feet. If you jump when the rope is at its apex, it will need to do 2.5 revolutions to go under your feet twice. If you jump when it's about to hit the ground, it only has to do two.
Making Speed with the Arms:
You want your wrists to do the work, not your entire arm. Revolving from the wrists is quick, from the elbows slower, from the shoulders, slower still. We want speed, so keep the arms quiet and the wrists fast.
Making the Rope "Short":
Keep your elbows at your sides and your hands where you can see them. If you push your arms out, you're effectively making the space inside the rope smaller, and you'll trip. If your hands are behind you, you're tensioning your biceps and slowing your wrists.