I absolutely love tutoring. From a few years of experience I have gained some knowledge on how to make tutoring a fun experience and not make students feel like they are attending a second school.
One of my main tips is to let the students set the atmosphere. They need to be comfortable in whatever environment to facilitate learning. If music helps them concentrate, or some kind of background noise, then encourage it. If they want to sit on the couch instead of the chairs, so be it. The student should be able to chose the medium in which they study so as not to feel constrained like a classroom setting.
Another tip that I like to give is to level. If you know that your student isn't going to understand something the way an Ivy League student would, don't use ridiculous words and techniques. The whole point of tutoring is to help someone understand a concept, not to show off how smart you are.
Subjects should never just be limited to the material either. Ask the student how they like the teacher, how school is going in general, their family. I've always found that the more of a connection you have with a student, the more apt they are to continue attending sessions. They see you as more of a friend than a teacher.
I also encourage on call tutoring. I'm not always available to meet with students whenever they have a question. So I encourage students to text or email me any questions they may have. That way, they don't feel so pressured to have all their questions prepared during a session. If they forget something, they can just call you when you're free.
My biggest piece of advice is to be prepared. There's nothing worse than showing up to tutor someone and they pull out material you aren't familiar with. It's embarrassing and a waste of everyone's time.