I've worked out how to fall asleep quickly, and this is my simple tip:
Basically I start to think/daydream about a fantasy story. Ie something completely irrelevant but interesting.
Maybe it is by coincidence or due to other factors like getting older or simply exhaustion but it seems to work evertime. And fails everytime I don't follow these rules.
So it has to be nothing realistic or related to my real life in anyway. If I think about something in my actual life I get too upset/depressed/happy/excited and very engaged into the thinking that I don't fall asleep.
So my rules are:
- Never think about what I did today or what I need to do tomorrow. That engages my brain too much and I can't fall sleep.
- Don't think about regrets of the past or problems in the future, again no sleep.
- Don't think about anyone you know whether romantically or aggressively. No good can come of that. Well maybe...
- Don't think about work or hobbies. You minds gets too active to fall sleep.
Think about something interesting that can not upset you in anyway. Which is best if it is something not related to you at all.
The famous tip of counting sheep  jumping over a fence works on the same idea, but never worked for me as it was too boring. I remember a tip on a radio show that also is similar; The lady said she "thought and concentrated" about each part of her body from toes upwards step by step till she felt asleep. Doesn't work for me but is again related to concentrating on something completely irrelevant.
My thoughts/dreams are usually almost like a Hollywood film. Something not related to my real life, but I "live" in detail in these worlds. Maybe because I am a man (with a vivid imagination) that my snoozethoughts are related to wild western / jungles / space / racing cars etc but they work.
I can continue the same story for months usually because I fall asleep so quickly so never really get anywhere in the actual story line!
If trying to sleep try to block out all other thoughts and imagine yourself living a life in a place like the Avatar film, then maybe this will work for you?
If you have problem sleeping, try it!
Don't think about anything in your real life, think unrelated fantasy, and zzzzzzz.