Character questionnaires are a great way of getting to know a character before writing a whole story about them. It is usually a very long list of questions that explore every aspect of the character's background. The exercise is meant to get the author to know every little thing about the character, but all of that information is not intended to go into the story. It is only meant for the author to know as background information to strengthen his knowledge of the tapestry and make the character more like a real person.
Put your character on the psychiatrist's couch and let her talk about her problems. Don't let her hold back. Let the words come freely and see where she takes you. This allows you to explore any of her hidden issues and problems. Act as a psychiatrist and "ask" her questions during this session. Treat it like an interview and ask things that come up. See what she answers in return. You may find that she has a lot of things to say that change the makeup of the character and the story.
Think of people who know the character and write out an interview with them. This can be anyone from her mother to her next door neighbor. It might also be interesting to interview someone who knew the character as a child to get insight into her behaviors back then. Fast forward to the present and interview the hero or villain to see how either of them feels about the character. This gives you insight into how the character is perceived in her world.
Write out a diary for the character or even an autobiography of the character's life. If your character has a particularly troublesome day in her life, have her explain it in her own words as a diary entry. This gives you the opportunity to see the situation from her eyes and feel it as she felt it; this is another way of getting inside the skin of the character and making her more like a real person to you.
Resumes, family trees and medical forms are all sources of information that a character could fill out to tell you about herself. A resume lets you know all about her job and how she sees herself as a professional. A family tree gives an overview of the family she is in and highlights any important familial connections. Medical forms that detail any health issues give insight into any possible medical background that may have been overlooked in the other methods.