Make sure it's the right girl. Don't get personal with someone just because you've been on a few dates or you're lonely. Ask yourself whether this is someone you can see yourself with long-term. If you can't see it, keep things light and uncommitted.
Pay attention to how she treats confidential information. If you've known her for two weeks and already know all of her friends' deepest, darkest moments, perhaps you're dating someone who can't respect secrets. Keep this in mind before getting personal. Establish your boundaries and encourage her to also maintain healthy boundaries.
Take the first step first. She might not want to scare you off by getting personal and could be waiting for a cue from you before moving closer. If you want to take the relationship to a deeper level, take the plunge. Tell her something personal and see how she reacts. If she reciprocates, you know you're establishing trust. Don't expect an immediate reciprocation. Give her a couple of days to get used to the fact that you're opening up.
Wait for the right moment. Telling her you have a poodle tattooed on your upper thigh might not be appropriate conversation while sharing a scoop of ice cream in a crowded restaurant. You'll know when the time is right.
Listen attentively if she tells you something personal and nod reassuringly. Reciprocate if you're comfortable. If you don't want a deeper relationship, find a tactful way to tell her you're not interested in going to the next level. Don't let her walk around thinking you're becoming emotionally close to each other if you really aren't.
Take it slow. Getting personal is an organic process and can't be forced. Telling a girl your whole life story on a first date (including embarrassing teenage locker room moments) can be a turnoff. You want her to know you're trying to get close to her in particular instead of blabbing all to anyone who'll listen.