How to teach

I was given the opportunity to be a math "teacher assistance" for 2 hours a week in high school. I will join the teacher in regular math class, though it is unsure what exactly this job will consist of.

I do want to have a first-hand impression of the level of the young students(age 16-17) and the education system nowadays in Israel and to observe how much, if at all, the level has fallen since when I was a high school student. However, my first goal is to learn about teaching, and how it can be done effectively.

I was partly inspired to start this discussion by a post on understanding that I was reading in this forum.I would like to here what your though on this subject of practical teaching.
--
* please move the post to a proper forum if needed.

As I said in that other post, the main thing is to get kids to understand rather than just follow procedures.  A derivation by itself may not be enough.  I like to visualize things, so a visual explanation helps.  It also helps to develop algebraic intuition.  This means being able to look at an expression and knowing roughly what its graph look like.  What happens when X is very big, very negative, zero, etc.

I home schooled my kids and used Singapore math books which are good.  I also managed to be a math major without ever taking probability, so I learned this on my own with this book:

https://www.amazon.com/Elementary-Introduction-Theory-Probability-Mathematics/dp/0486601552/

This Russian book is an excellent example of what good high school math could be.