Prerequisites for Forcing

Kunen's book "Set Theory: An Introduction To Independence Proofs" is pretty much self contained and one of the standard references on the topic, depending on your background in set theory you can skip the first chapters. Strictly speaking the prerequisites for forcing are not much, but for it to make sense and be motivated you should be familiar with some set theory, as presented in Kunen's book for example

I am a big fan of Halbeisen's "Combinatorial Set Theory: With a Gentle Introduction to Forcing".

The only issue there is that Halbeisen is forcing "up", that is, $p\leq q$ means that $q$ is a stronger condition. This is something a lot of people are moving away from these days (although not everyone). So this is just something to be aware of, when you start reading other people's forcing proofs.

Other than this, a quick bang for your buck would be Jech's "Axiom of Choice" book which has a speedy exposition on set theory (skip Chapter 4 if you're interested in forcing), although it mainly focused on methods related to the Axiom of Choice, and at the end of the day, most actual proofs "in the wild" do not use Boolean-valued style arguments. It can still give you a good basic idea on what is going on. His "Set Theory" book (3rd edition, of course) is a great book as well.