How do I approach a novel like Animal Farm?
There is no one way to approach literature. The best way to approach literature is to do so in many ways. As you do this, you will learn more, see more, and appreciate the artistry in great depth.
When it comes to Animal Farm, first I would read it as a story. In light of this, ask yourself, what is the plot? Where is the tension, the climax, and the resolution? Who are the main characters, and what do they do? You would ask these questions of any work. So, do so with Animal Farm.
Second, read it as an allegory. What or who do the animals represent? The pigs are obviously the leaders. Boxer is a faithful laborer, who is used and then discarded. Mollie may represent the aristocracy, who like the finer things in life no matter what is really going on.
Third, you should read the book as a historical commentary of what was going on in Orwell's time. When we do this, it become a political commentary on communism and capitalism.
I agree with "readerofbooks" that it is an allegory. As such, I would approach it with a dual mindset; that of a futurist and that of an historian. As you are reading, think about the state of the world today and how it might be in the future. Ask yourself if Orwell was prescient, or just a social cynic (or both).