Firstly I will need to know what they want to be privately taught in the first place, so I prepare a slideshow + a quiz on the topic.
Always a friendly introduction, make sure I approach their query as a doctor would; I am after all, there to help!
In the sessions(s) I will tend to ask what they know already about a certain topic, to get an idea of their knowledge on a certain topic.
I will then be teach them slide after slide the topic of interest, and make sure after each slide or so to question them on what we have just learnt, in a calm and patient approach.
After that we will do a quiz; the size of which will depend on the breadth of topics we are covering in any single session, before ending the session; finding feedback.
I will always provide additional reading to help them understand topics further and thus bolster their learning.

Ive often found an immersive technique to be the best way to make students remember topics, such as roleplay; e.g I am the student and they are the student, or they need to present to me a short 3 minute presentation to teach me X,Y,Z etc.
I have also worked as a gym instructor in the past, so I find issuing a good balance of friendliness as well as teaching can make the student(s) feel like they are not being "taught" in the traditional sense; rather, that they are with a study buddy, and we are both revising for an exam.