That "how" is a hard question to answer fully, because it applies to the entire book.
He uses the fable form to satirize humans in general, by giving animals human characteristics. The book itself is a satire on the Soviet revolution, with the different waves of political organization mocking the waves of revolution and reform that swept through the U.S.S.R.
He uses the reasoning of specific animals to satirize specific political parties and positions, as well as social ones. For example, Moses (as the name suggests) stands for religious visionaries and the bird plays a role like the one ministers do in our society. Boxer represents the working class who try to deal with thing through hard work and ignoring politics.
The biggest single satire and allegory is in the transformation of the pigs. The pigs (communist revolutionaries) set out to completely overthrow and change the system, and in the end they were as bad as the humans (czars).