I am trying to understand divisors reading through Griffith and Harris but it is difficult to come up with any particular interesting example. I have browsed through Hartshone's book but everything is expressed in terms of schemes, and I believe it is still possible to find some toy example to carry with me without having to learn what a scheme is first. Does anyone know any reference or book which has some exercise or example on this? In particular I would like to see examples of linear systems of divisors and how given a linear system of dimension $n$ I can choose a pencil inside it.
Apologies if this is not the place to write this, it is my first post. I have searched through the questions and have not find anything similar.