How do you build a student's confidence in a subject?

I like to first work through problems step-by-step, asking questions at each step to make sure they are following along. This will quickly reveal any weaknesses in conceptual understanding. Then, I walk the student through a similar problem without just telling them how to do it. Next, I have the student try a problem on their own. Working through different problems that require different skills teaches the students that they are capable of learning new material and are able to apply it, which helps them feel more confident and capable in the subject.

How do you evaluate a student's needs?

I generally start by briefly getting an idea of the student's academic history: what subjects they have taken recently, what they like and dislike, and what has been giving them trouble. If the student does not have a specific concept or skill in mind already, then I'll use this to pick a good starting place. I generally first give simple problems to see if they understand the skill well enough conceptually to use it in basic contexts, and then move on to more complicated problems, based on how much the student struggled.

How do you adapt your tutoring to the student's needs?

For any concept, I always try to have several different ways of explaining it, and I choose which explanations to use based on what has worked for the student in the past. For instance, if the student seems to be more of a visual learner, I might show them a graphical way to solve a problem instead of a more algebraic method.