How do I make my girlfriend open up to me and tell me what's on her mind?

You may talk to her about it, but you must be careful, or she will totally shut up. If you really love her, you won't "make" her do anything against her will. Tell her you'll be patient, if she's not yet ready to confide in you as much as in her (perhaps old) friends (old not meaning age, but the time she knows them. Today people are sometimes gf/bf after few months, even weeks, as Y!A often tells).