What's her favorite band?
What song sends a feeling of melancholy into her heart?
Music is important to most people. It weaves in and out of our lives- the every-days and the major days. It can do that for our characters too.
That may mean it appears in our stories or it may mean that it's only in our minds as we think about our characters. I find it enhances my creativity as I develop my characters. Or rather- it helps my characters reveal themselves to me.
I learned the magic of music in characterization back when I was writing H.P. fanfiction. My stories were drivel, but I learned to take minor characters and developed them into complex people and I've applied what I've learned to characters of my own creation.
Now sometimes your characters will enjoy the same music you do, but often you explore in order to discover what makes their toes tap. If you have others in your house to supply you with a variety of music flavors, you're lucky. Otherwise, you must flip through radio stations or the internet and go where you wouldn't usually find youself.
I had a teenager in the house while writing my novel. I was privileged to be exposed to some unique local bands. My characters actually go to a Cold Hot Crash concert. I got to go to one of their concerts. Immersing yourself in the culture, sports, art, locations, et al. of your characters is super, but that's a topic of another blog.
While writing a particular scene, my teenager was playing a song by another local band, Flamingo Gunfight. It was eerie how perfectly it fit the scene. I decided to let the character sing the song to himself. I later rewrote the scene and removed the lyrics because you can't really do that without permission. It was brilliant, though. Maybe I should ask them for permission. If/when I get a publisher I'll ask what sort of permission I'd need.
Anywhooo, my characters live in my area- San Francisco Bay area, so, I have access to the same things they do. But maybe you're writing an historic piece. Immerse yourself in the music of the era. Find out where to hear live music if possible, but recorded is good too.
Perhaps your character likes music outside of his or her time. They like older music. Just because she's a modern teenager, doesn't mean she doesn't like ragtime or blues or classical. What I'm saying is, you don't have to stereotype your characters. Have fun. And it may or may not come up in the story itself, but you will know and it'll add to the development of the character.
A note on your own mood.
Music can help you get into a writing mood. A song can invoke a feeling when you're trying to write a difficult scene. Even if you don't like to listen as you write, maybe take a walk or clean the house and listen to the mood music before you sit down to write. Just don't write in the same room as your daughter while she's listening to a very emotional song over and over and over or you will write utter melodramatic poppycock and have to toss it out. (I speak from experience. Ick)
Oh, and one more thing. Did you know that Mad-Eye Moody's favorite song is Procol Harum's "A Whiter Shade of Pale" just like mine? How about that. ;)