"I will lie in bed, awake, forever thinking and rethinking whatever happens to be on my mind at the time."

I can sympathize. I used to have a ton of trouble falling asleep until I learned some basic meditation techniques to shut off the inner dialog.

I quite literally focus on turning off my brain. I'm not really doing that, of course, but that's how I visualize it. With a little practice you can drift off at will.

Also, I read once that the meditation masters would carry a bamboo stick for students that fell asleep, for a good reason. :-)