There's a lot of truth in music. Not only does music offer classic, universal advice ("You gotta know when to hold 'em, know when to fold 'em, know when to walk away, know when to run,") it also offers just plain good writing advice: "You gotta dig a little deeper if that girl [book, story]'s a keeper." Here are a few questions that will help you to dig a little deeper and get to know your characters:
Does this character have brothers or sisters?
How important are family relationships to your character?
What does your character do for a living? Is this job temporary or a career?
Is work important to your character?
Where does your character live?
How is your character's house/apartment/room decorated?
Does your character have a pet?
What are her important possessions?
What are his hobbies?
Why does he wash his socks on Sundays and underwear on Tuesdays?
Does she own a vehicle? What kind? Does she know anything about it?