Tell your student about yourself first. You can't expect her to let you get to know her if she knows nothing about you. Share things such as information about your family, your occupation and your hobbies or interests.
Ask your student questions that will help you to learn more about him. These types of questions include inquiries about family structure, likes, interests and friends. Ask school-related questions as well, such as what subjects or assignments seem easy versus which ones seem difficult.
Give your student a checklist type of questionnaire if necessary. This is useful in situations in which the student is a bit shy and doesn't want to talk about herself very much. Ask the same sorts of questions that you would in a verbal interaction. The only difference is that you write the questions and provide multiple choices from which the students can choose. If your student can't read, then read the questionnaire for her.
Talk to the student's family, friends and teacher. They can usually provide valuable information that will help you to tailor your tutoring to suit the student's unique needs.
Ask your student to draw a picture that describes himself. This is especially useful for elementary students who may not have developed advanced verbal or writing skills. You can ask the student to describe the picture to you so you can learn more about him.