I take melatonin every night, and have been taking it for at least 15 years. The only time there's ever a "hangover" effect is if I take it when I have to be up very soon, such as taking the pills at 4AM when my alarm is set for 6AM.
If I take it at least 30 minutes before I plan to sleep, it takes effect gradually and as long as I get 6+ hours of sleep, I don't have any problem waking up or any lingering effects.
Alcohol can help in SMALL amounts. I think anybody who advocates taking more than 1-2 drinks is nuts -- I mean, drinking more than 1-2 drinks can be fun, and getting really drunk might even help you to sleep, but you won't get good quality sleep and will wake up feeling tired.
I agree with Immersion about the mental aspect of sleep. Usually it's a "racing" mind that prevents me from sleeping. Don't allow yourself to do anything stressful or anxiety-causing for at least an hour before you try to sleep. In other words, don't play exciting video games, and then shut off the light and try to sleep 2 minutes later.
Anything you can do to gradually slow down, decompress, and diminish stress leading up to bedtime, will help.