Skipping rope just get's easier with time, but it's something you really have to keep at like a speed-bag. switching feet like boxers do can help (it makes it easier to skip for longer focusing more on hand eye coordination) opposed to jumping off both feet each time. you want to focus on your wrist movements, keep your knees straight and you don't need to be jumping high. keep it all in the wrists and the speed of the rope. If you are hitting yourself with the rope, hitting your ankles, missing skips, the only real solution is skipping more.
try to build up to 12 rounds of 3 minute intervals, building up to that, you just naturally get better. It's an issue of hand eye coordination and muscular endurance. Working the abs/calves will allow you to skip for longer if you find it's an issue of muscular endurance.
If you get to the point where you ever find skipping easy, you can skip with a weighted vest or weighted skipping rope. Though skipping by itself is so good, it may never be needed. practice, practice, practice.