George Orwell describes the events of the novel in a straightforward way. He does not comment on the motives of the characters. How does he use irony to make the reader understand what is really going on?

Irony refers to the incongruity between what is expected and what occurs. In the Animal Farm, three types of irony have been depicted.
Situational irony is Animal Farm is manifested in a significant way. Having been slaves for a long time under the human dictator (Mr. Jones), animals now want to rule themselves. Even though animals do not like the human nature of doing things, they still end up doing much like humans. At the end of the novel, pigs adopt the human character in that, they eat apples, sleep in beds, and trade with humans which is contrary to the principles of Animalism.
Verbal irony is a figure of speech in which what is said is the direct opposite of the intended meaning. In this context, verbal irony is understood when Boxer is being transported to the slaughterhouse. Although the van has apparent inscriptions that read, "Horse Slaughterer and Glue Boiler," Squealer tells Boxer (who is apprehensive) that he is being taken to the hospital.
Dramatic irony usually occurs when the reader knows something that some characters in the text don’t. In Animal Farm, the reader is aware of the changing rules since they can read. On the other hand, animals are illiterate and gullible. Hence, pigs, who are intelligent overrule and exploit the other animals.
The use of irony as a figure of speech has substantially helped George Orwell to relay his message. It is rational to conclude that the use of irony is meant to deride communism and dictatorship that was portrayed by the Soviet Union.

In Animal Farm, George Orwell lets the narrative itself convey his message on the dangers of totalitarianism and populist uprisings. Orwell did not need to explain the motives of the characters, because we the characters—particularly the pigs—transform into human-like creatures.
Orwell uses irony by illustrating the "evolution" of the pigs—especially Napoleon and Squealer—from disgruntled abused animals to becoming abusers themselves. For instance, Orwell frames this evolution by showing the negative traits of men. Orwell depicts the farmers as drunk, abusive, and lazy. The humans represent the old aristocratic regime which did not care about the welfare of their subjects. The animals, at the beginning of the story, represented the oppressed citizens of monarchies. The Battle of the Cowshed is similar to the civil wars and revolutions of men throughout history. The act of going to war itself showed that the animals were becoming human-like.
In the middle of the story, Napoleon began to exhibit negative traits of people: greed, sociopathy, and vengeance. Likewise, Squealer began to lie to the other animals, an act which represented the spread of propaganda in the real world. The act of lying is a human trait. These are some of the examples of the pigs' transformation. Even Snowball showed human characteristics, such as having progressive ideas and believing in infrastructure.
By the end of the novella, the pigs are wearing human clothing and carrying whips to punish the other animals. This final scene is the ultimate illustration of Orwell's use of irony in Animal Farm.