Learn French: Il ne comprend pas le professeur. - He does not understand the teacher.

French doesn't use helper words like "do" or "does" to make a negative sentence. You just frame the main verb with ne and pas. So, "does not understand" translates simply to ne comprend pas.

Why did we use ne here instead of n'?

You only shrink ne down to n' when the verb right after it starts with a vowel or a silent 'h'. Because comprend starts with a consonant, ne stays exactly as it is.

Why does comprend end with a 'd' instead of an 's'?

This is the specific spelling of the verb comprendre (to understand) for the pronouns il (he), elle (she), and on (we/one). If you were saying "I understand" or "you understand", you would use comprends with an 's' at the end.

What if the teacher is a woman? Is it still le professeur?

Traditionally, le professeur was used for both men and women. Today, people also use the feminine version la professeure for a female teacher, but you will still often hear the masculine form used for everyone.