I have a compound sleep disorder that leaves me acting like I have insomnia. I've been successfully using these strategies every night since I was a child (with a few periods of extreme flare-up, where they were of limited use).
First, don't lie in bed for more than 20-30 minutes. If you're not going to sleep, there's no point in torturing yourself over it.
Find something mindless to do that will tire your eyes. I'll either browse Imgur on my phone in the dark, play Sudoku, or read the same old stack of comic books (actual comics, like Calvin & Hobbes) by nightlight. The most important thing here is that you don't have to get up to turn off a light, or do anything at all except sleep when your eyes can't take it anymore.
If that isn't working, or I'm in a bit of a rush, I'll organize things in my head. When I was a kid, my mother would give me a letter when I went to bed. I'd start at that letter, and put all the countries in the world in alphabetical order, starting with that letter (the new letter, so you don't get too bored with the A, B, & C countries. If you don't know your countries, try rivers, flowers, car models, actors, whatever. I stick with geography most of the time still because it works for me (except now, I tend to pick my own letter!).
If I feel the need to sleep starting into a bit of a panic, I'll put fresh sheets and pillowcases on my bed, take a hot shower (leaving my hair dry), let my mind wander as much as possible, and try again.
