What is needed to arrive at Bézout's theorem in Algebraic Geometry?

Question

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