How to tutor? This is a topic that every tutor approaches differently, and yes, there are many different methods, but what makes a tutor successful are some key underlying principles.
A good tutor knows their subject inside out; however, an excellent tutor understands their student and their individual learning requirements as well as the subject. Tutoring shouldn't be like school, where a topic is taught to a large amount of students making the approach more generalised. A tutor's role is almost the opposite of a classroom teacher: to give an individualised experience that directly addresses a student's weaknesses and in the process builds up their confidence so they are ready to achieve their goals.
The best tutors also go above and beyond to make learning fun, whatever the age group. A lesson with a private tutor shouldn't feel like a chore. Tutors have the flexibility to tailor lessons to what the student is interested in or enjoys doing while still covering the content. For example, if a student really enjoys making art, their tutor can incorporate this into their homework and have them make a poster on the topic covered in the lesson or if a student is into a sport, this can be worked into teaching materials etc.
Tutors also have the scope to go above and beyond the initial school or exam specification, if a student is interested in a topic. This allows students to understand the "why" of what they are learning. By understanding why concepts work and deepening their understanding they are more likely to remember the content and subsequently perform better in their exams, be more prepared for the next stage of their education and enjoy the subject more.
As a science tutor, I have had some great discussions with students about things on their specification that I have studied further at university, purely because they wanted to know more. Due to this they understood the topic more than their peers and when going back to the syllabus, they knew above and beyond allowing them to answer exam questions on the topic with ease. Of course this is not a technique that can be used on every topic but fostering that excitement to learn in a student should be a key part of a tutorial.
Ultimately, this all circles back to each student being an individual and the luxury tutors have of being able to put this at the centre of their teaching. This is at the heart of why tutors love what they do, they are able to make a real difference to a student's education as they are able to focus solely on them for an entire lesson. By treating every student as an individual, it then makes it easy to build rapport, and with this comes engaging and fun lessons which almost always directly correlates to academic progress.