The verb "avoir" is very important in French as it expresses having or possession. To properly learn French, students must memorize the present tense forms of "avoir" like "j'ai, tu as, il a" and negative forms like "je n'ai pas" through repetition until they can say them quickly. Mastering the present tense of "avoir" is essential for expressing what one has as well as the past tense, and it is important to use "pas de" rather than "pas" when expressing not having any of something.