On days that I have to get up early I usually have insomnia the night before. How to fix this problem?

See below. I agree with dr. Varghese-guided imagery & muscle relaxation exercises help. I'd also add yoga & yoga breathing exercises. Your public library may have yoga dvd's you can borrow;they're also available online. Eliminate any caffeine products after lunchtime, too. If you still find your mind racing at bedtime, write everything on your mind onto a notepad before turning lights off to clear your head.
Warm foot bath. A warm foot bath or anything to help relax you is helpful. You may try magnesium as a natural element to help you relax as well.
Anticipatory anxiety. Patients often comment on having some brief insomnia before an important meeting or appointment the next day. Sometimes, they put themselves to bed at a time when they are not sleepy. This may result in frustration if they can't get to sleep and stoke a "racing mind". Try guided imagery, passive muscle relaxation, and a bedtime snack. Most important don't worry.