Make some initial small talk. Find out where the student is from, where s/he lives on campus, what other courses s/he is taking, etc.
Tell the student more about your own experiences with the material. You may talk about your major, courses/professors you've taken before, etc. While you don't want to appear overconfident, talking briefly about your background may help the student trust your ability.
Find out why the student is in the course. Maybe s/he is taking French solely to fulfill a distribution requirement or maybe because it's relevant to the art history major. Maybe s/he is taking Logic because it's required for a Philosophy major or maybe just because a friend or advisor recommended the class. Essentially, understand your student's academic position, goals, reasoning, etc.
Ask the student to talk about the course and subject matter you will be tutoring. How does s/he feel about the professor? Is s/he aware of the areas needing attention or is s/he totally "lost"? Try to gauge the student's comfort level with the material, his/her degree of preparation, and his/her strengths and weaknesses.
If possible, find out more about the student's learning style. S/he may be able to tell you under what conditions or with what approach s/he usually learns best. If you so desire, the CTL has many resources to use as stepping stones to help you and your tutee understand learning styles in the initial sessions.

Tips for successful sessions

At the start of a session, find out how things have been going since the last time you met. How did the quiz go? Which new concepts were introduced in class? Is there a new assignment? If you have a bad memory for things like this, consider taking notes during the session to remind yourself on what areas to follow up on.
Set an agenda for your session. What specifically do you want to cover? How much time can you both devote? Do you want to devote the first half to explaining the material and the second half to practice? Is there a particular assignment to go over?
You may wish to begin with a review to reinforce what the student already knows and to start with a point of confidence.
Focus on one concept of idea at a time. Sometimes, a student may need help understanding several complex and/or interrelated ideas. Help the student identify and separate steps in a process, different skills/ideas, etc.
Try leading by example. You may wish to do a practice problem or two and then ask the student to do one him/herself, using you only as a reference.
Ask the student to verbally explain the concept or problem--conjugating the verb, completing the proof, etc.
In general, ask questions. Especially if the student is starting to get stuck regularly, make sure you ask enough questions so he/she figures it out him or herself.
Be patient, giving the student adequate time. Remember that silence is okay as it allows the student time to think/analyze.
Be flexible in your approaches. Try visuals, flow charts, analogies, mnemonic devices, repetition, etc. Ask the student which methods generally work best for him/her
End the session with a short summary of what you've covered. This not only helps the student review concepts but also instills a sense of accomplishment.
End on a positive. If you're working on the most difficult concepts last and the student is struggling, return to areas with which s/he feels more confident.
Talk about scheduling your next session. During this conversation, set some goals or ask the student to work on specific concepts before the next session.
Offer the student a chance to give you feedback!

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