It doesn’t matter in which field your expertise is, weather it’s Math or History, Physics or English or even Piano. There are several matters to pay attention to, and once you do that - your work should be a lot easier and your satisfaction should rise as well :)
it doesn’t actually matter in what way you describe a certain topic, what matters is how you implement it; the implementation is super important because that’s how students in specific, and people in general tend to remember stuff.
So whatever it is that you’re teaching, the plain theory in the background should stay in the background, and what matters most is the implementation.
If you teach a new algorithm in computer science- write a small program to show its implementation, if you teach a new method in grammar - use sentences to make sense of it.
Even if you teach history or law - try to find examples to make the topic more interesting.
That advice refers especially to complicated and complex ideas and theories- in computer science. In high level math (like calculus, linear algebra and more), in psychology, biology etc. The human mind is far more comfortable comprehending wide and abstract ideas when they’re simple and small- the smaller they are, and the more pieces they are broken into - the easier it’ll be for the human mind to grasp that idea.
When explaining an idea, especially if it’s complex, be sure your student, or listener is following you, and understands each and every step in your whole idea. It’s very important and even crucial, not to miss any idea, any stage, and decision making in how to reach a certain stage on the way of obtaining the solution.
When tutoring a topic with lots of text and details to remember (like History or literature for example) frequently, along the way, the student may forget some of what you’ve earlier taught them. To avoid this situation, please be sure to repeat every once in a while some random part of the text, to discuss it again, so there will be a chance and a challenge, to comprehend and rehearse the whole idea over and over again, from time to time.
There are more than one subject in which the student should digest a large amount of information at once, so when you teach someone such a subject or a concept, be sure to keep that in mind.
Try to put yourself in your student’s place - think of what he or she knows, of how his or her logic works, and try to structure the ideas and principles you should teach accordingly. Try to understand the body and facial language of your students and to follow their lead, with consideration to the process they’re going through, on their way to understand what you’re trying to teach.
For both practical and psychological matters and needs, be sure to mix both hard parts and easy parts of the syllabus in your class or tutoring session. The advantages are huge - on the one hand it lightens up the whole energy and vibe of the tutoring session, and on the other hand it helps the student in believing that he or she are hands on the lesson you’re trying to teach them.