Yeah, definitely not an anti-anxiety supplement! Melatonin is the body's natural sleep hormone. When you take it before bed, you get a window of sleepiness that makes it easy to fall asleep (but if you're like me, you can work right through that...)
I take melatonin when traveling mostly, to get to sleep on a normal-ish schedule after changing time zones. I've also used it just as a sleep aid at home, but not regularly. I take a 3mg tab when I use it, and just like onlymedid, it knocks me out and I feel great in the morning.
I'd suggest asking your doctors about something for anxiety, since this really isn't going to do the trick. There are a couple of natural supplements that are supposed to help with sleep, anxiety or relaxing, but you still need to be careful that they don't interact with any other meds you might be taking. Valerian and St. John's Wort come to mind. Apparently Kava kava is not recommended anymore, due to reports of liver damage.
Chamomile tea is always safe, though!