I am actually a quiet person too and shy type. Im not expert on this but I'll still try to answer your question. Well just feel relax, feel comfortable with the person you're with. If you're uncomfortable, the person will feel the same. So just be your self. Maybe you start ask your date about herself that you want to know. Maybe you can start with her favorite movie of tv show or hobby. And try to share something about you too but don't share so much about your self. Coz sometimes people get boring when they started talking much about themselves.