I had this problem when I was a kid, and my oldest daughter has it, too. My youngest, though, is just like her dad- falls asleep when she's ready, even if she's not that sleepy. I think some people are just wired this way. My oldest will complain that she can't get to sleep, and I know she's telling the truth because when I go by her room she's just staring up at the ceiling, looking bored, even if it's 11pm.
I can only tell you what works for me personally, and what doesn't work. First of all, music. This did not work for me, because instead of soothing me into a slumber I'd get caught up in the melody. This would actually keep me awake longer, flipping the cassette tape over repeatedly well into the morning hours. If you want to try music anyway, pick something boring and unfamiliar and switch it out often.
White noise helps a lot. You can get a machine that makes it, or just crank the ceiling fan up. I have to have a ceiling fan, even in the dead of winter, because I need the noise. Which also means that it can't be thumping or moaning like some ceiling fans do, because that negates the white noise.
Make sure she has comfortable bedding- a good pillow and a soft blanket. Again, speaking for myself, I prefer heavy blankets over a plush blanket. The weight is somehow soothing, and the softness keeps you warm and makes you feel snuggly.
Lots of activity can't hurt, but it's not that simple of a solution. I was very active in high school and college, both physically and socially, but still couldn't get to sleep at night. My daughter is the same way. We went to a pool party once where she swam for FOUR HOURS, and I thought surely this will do the trick. But no, she was still awake after bed time, staring at the walls and drumming her fingers on the blanket.