How do I get a very close friend to start opening up to me about her personal life?

I think its great that your so open with your best friend. I think you should simply ask her. Ask her if anything is wrong. Asking her is the best way. Ask her what's up in her life, or say that you feel tat because your best friends then you should tell each other about your lives. Best of luck.

please consider this: different people have a different need in 'being open', and we define 'being open' quite differently, too. maybe your friend feels satiated just spending time together with you. or maybe she is content with just mentioning the news, without analyzing them. what i mean to say is that she doesn't necessarily keep secrets from you; perhaps her way of experiencing life is merely more laconic. :) and if there's anything in particular that you'd like to know about her, you can just ask, right?

Well, it depends on what you want to know. If your friend seems depressed than don't ask her questions about her personal life, saying things like "Are you okay?" or "How are you going?" are better questions because then she won't feel like you're trying to be a sticky-beak. If she doesn't want to talk about it than I think it's either a bit personal for her or maybe she needs to earn more trust.

Assure her that you'll be there for her as much as she is there for you. Slowly ask her more personal question but be careful not to push too hard. Make them feel like you're very interested with their life situations and that you are trustworthy.