abstract algebra – What is needed to arrive at Bezout's theorem in algebraic geometry

I'm doing a paper that deals with Bezout's theorem, I'd like to do something from scratch, showing everything I need to prove Bezout's theorem and give some examples of this theorem. My question is, what should I do or what should I enter to prove Bezout's theorem and discuss examples? Initially, I thought about introducing related varieties and projective varieties and then enunciating Bezout's theorem. (It should be noted that I still do not master the subject well, so the job is also to learn and understand all these things at the same time, therefore, I need help with what I should copy at work). Thank you.