One of the things I find incredibly useful to do is write characterization exercises. (Or detail exercises, or dialogue exercises, or activity exercises.) These generally don't get shared because they're not usually pretty, but mostly because they're just not meant for others' eyes. Writing exercises like these help you find your voice and develop a strategy for dealing with some aspect of your writing in a larger, meant-for-publication piece. I suggest picking a word count--500, 1000, or 2000 words are good numbers--and going for it.
1. A car breakdown.
The way a person behaves when their car breaks down tells you a lot about them and their history. Is this a regular occurrence? Are they used to it? Did they prepare for it? Where it happens can provide a nice exploration of character. Is it on the side of the road between cities? In a bad part of town? Near home?
2. Preparing for a parent's visit/going to visit parents or in-laws.
Unless your character is a single orphan, family will probably visit her at some point. Or she'll visit family. It doesn't have to be an overnight visit. Maybe her dad and his new wife are just popping in on their way to dinner, or maybe her mother-in-law is doing one of those surprise inspections on the new housewife. Whatever the case, there's a lot of emotion and a lot of character rolled up in how we deal with parental figures.
3. A first date.
I'll confess: I hate dating. I went on maybe four dates during my "high school" years and I didn't date at all in college or for about a year and a half after college. And even then, I got married eleven weeks after meeting a guy (ten weeks after our first date). But I hear some people like it. And I understand that most people don't meet someone and decide to marry them three weeks later. A first date for your character is kind of the same thing as a first date for you. You're going to learn a lot about them based on how they present themselves, what they worry about, what they ask, what they notice.
4. A job interview.
This is sort of the same as a first date, just with an added layer of professionalism. Is your character prepared for the interview? What does she wear? How does she feel? What does she say? What's her attitude about being there? (Is she being herself or is she trying to be what the interviewer wants?) Does she need the job? Does she want the job? A job interview for a character will probably show you how she behaves in the most stressful of non-intimate situations.
5. The first time your character had sex.
This is an old one and maybe kind of cliche, but it's a good one. You remember your first time. It's kind of a defining moment in a person's life. Your character is a person. And, not to get too triggery here, but if your character's first time wasn't consensual, or if your character's first time was maybe plagued with doubt and regret, you're going to learn a lot about him.
6. Doing something that frightens her.
I am utterly, completely terrified of "fun" houses. You know the ones. With the mirrors. Or the dark ones with the people in costumes who don't touch you but make damn sure they chase you. Shaking, crying, full-on panic attacks. Which is weird for me, because I am the least-easily-frightened person I know. This includes my Army husband and retired Navy/cop father. Bugs? Icky, but okay. Snakes? Respect 'em. Bad guys? Try me, buddy. I've been through a lot of very real, very scary stuff in my life. But fun houses reduce me to a small, scared, whimpering child. Throwing a character into a situation that scares her is going to reveal a lot about who she is and some of the most primal inner workings of her mind.
7. Winning the lottery.
It's an ultimate fantasy situation, like getting a chance to spend the night with your favorite celebrity (*coughTimArmstrongcoughyesIknowIammarriedandnoitdoesnotreallymatterIwouldtotallyhitthatcough*). But if you take the fantasy part out of it, there's some real conflict there. How does she react when she finds out? What does she do with the money? Who does she tell? How does she react to people coming out of the woodwork? Does it help or hurt her goals in life?
8. Home alone on a dark and stormy night.
Come on, even the bravest and most jaded among us can get a little spooked all alone in a big, drafty, silent house in the middle of a terrible storm. Or maybe she likes to cuddle up on the couch with fuzzy slippers and hot chocolate and read herself Edgar Allan Poe. The point is, it's a mini-isolation exercise. How does your character fare, think, act when she's completely alone?
9. Confronting someone who has wronged her.
Is she into the guns-blazing kind of confrontation? Is she subtle and manipulative, drawing out the confession before she acts? Is she passive-aggressive? Is she passive? Is she aggressive? Does she have control or does she let her anger/hurt control her? Confrontation is powerful. Facing the person who has done you wrong is a highly-charged moment. Is she a fighter or a flier? Write and find out!