To give the subject some meaningful context, I think it would certainly be useful to begin a topic by first discussing its benefit. After that I would go through some easy instances. I should stress that there are no silly enquiries, anything to aid a tutee's comprehension is essential. After I've run through a couple of examples, I would love to have the student run through their personal instance, talking to me pretending they were the tutor and I was the student.
Lots of researches have revealed that trying to explain a principle you have actually a while ago learned helps profoundly in memorisation as well as comprehension. If I'm satisfied with their teaching, I wish to examine their critical thinking by setting an issue based on whatever found out in the lesson, but with refined changes that require the student to proactively involve with the work, instead of be on "autopilot".
Home task will certainly be set on the material reviewed (nothing too extreme), and even more lessons will be spent answering exam-styled questions before carrying on to the next topic.
During lessons I would love to urge a relatively informal, friendly atmosphere. I have a good time training, as well as I hope students enjoy my training sessions, and also an unwinded mind is better at studying.