The duties and responsibilities of a tutor can vary from community to community (or between individual tutors) but the basics remain the same.
The tutor needs to find out what the issue is that is causing the need for tutoring. Sometimes it is obvious, like a failing grade, and sometimes it is not as easy to pinpoint–like a motivation issue, or test anxiety.
Next, the tutor needs to help the student reach his or her goals by overcoming whatever the issue is. This work may include talking with the student about the issues he/she is having, re-explaining topics or concepts that were covered in class, working on homework together, helping develop sound study skills and time management skills, giving extra practice, and teaching the student how to study for tests.
Finally, the tutor needs to check in from time to time to see if the tutoring approach is working. Although grade improvement can take some time, there should be other subjective improvements like attitude change, more participation, and higher quality work.
Good tutors are good communicators, and they generate rapport and a solid connection with the student. This is important to the success of the tutoring. This is why a tutor should be passionate about tutoring, or the student will sense that the tutor is not sincere, which could undermine the support.
Also, it is important to consider that if you are tutoring in the home, a tutor should have a policy that a parent or guardian needs to be home during the tutoring.