Find the right place between the lines: as a tutor, you are neither a parent, baby-sitter, traditional classroom teacher, nor sports coach. The role is unique.
Be flexible. Adjust your lesson plan if it's not getting across the concepts to the tutee. Notice how they have fun and incorporate that into learning - there's even more freedom than in the classroom. Use your own personality to be the best tutor you can be, and remember that it's your job to teach, coach, encourage, clarify, and listen, but not to DO the work for the tutee. The student is responsible for his or her own learning.