A few things you can try without doctors or pharmaceuticals: warm milk, or chamomile tea before bed. Cut out all caffeine at least 3 hours before bed - the earlier, the better. Take a warm bath or shower to relax yourself, but set your room temperature to be cool (but not uncomfortably cold). If you aren't allergic, try a lavender-scented air freshener.
While in bed, try slow-breathing. It's not exactly meditation, but it can help your body hit some of the same triggers. Inhale slowly for a count of 3, hold for 3, then out for 3. If you're a side-sleeper, put a pillow between your knees, or under them if you're a back-sleeper (helps with spine stress).
Important thing to remember, once you are asleep: Do not turn on an overhead light until it's actually time to wake up. Invest in a night-light (15w bulb) for the bathroom if you worry about running into things. If you turn on a 'daytime' level light, it shocks your system into 'wake up' mode.