Book Suggestion - Complex algebraic surfaces

Question

I am studying for an exam of algebraic geometry, in particular, I am dealing with ruled surfaces and numerical invariants, rational surfaces, Castelnuovo's Theorem and its application. I am reading the Beauville's book "Complex Algebraic Surfaces", but I realised that I need some introductory books first. I need a book that could help me understand Cech cohomology as an instrument. Moreover I'm finding difficult to understand the concept of exact sequences of sheaves, their application (e.g. in the proof of Noether Enriques theorem) and their relation to divisors. Without these notion I cannot understand the proof of Castelnuovo contractibility criterion, the Noether Enriques theorem and another theorem concerning minimal surfaces, which are some of the main theorems of the exam. My basis knoledge is the Rick Miranda Book, which I sudied deeply. The Shafarevich and Hartshorne books are not helping me. Some suggestions?