In verbal irony, words mean the opposite of their intended meaning. In situational irony, events unfold in ways opposite of what might be expected. In dramatic irony, the reader or audience knows something the characters in a work of literature do not.
An example of verbal irony occurs when Squealer describes Napoleon taking dictatorial power as a "sacrifice" he is making for the good of the community:
I trust that every animal here appreciates the sacrifice that Comrade Napoleon has made in taking this extra labour upon himself. Do not imagine, comrades, that leadership is a pleasure!
Of course, despite what Squealer says, being dictator is Napoleon's (and the other pigs') chief pleasure. The most famous example of verbal irony is the way the pigs twist the meaning of the word "equal" to mean unequal.
An example of situational irony occurs when the cowardly Napoleon, who hid during the Battle of the Cowshed, decides to award himself both the Animal Hero, First Class, and the Animal Hero, Second Class medals while at the same time declaring Snowball a traitor. In reality, Snowball fought bravely and the real traitor to the ideals of animal farm is the power-hungry Napoleon.
An example of dramatic irony occurs when the animals hear a loud crash and come out to see Squealer has fallen from a ladder and is sprawled beside a "lantern, a paint-brush, and an overturned pot of white paint." The animals are not able to understand what this is all about:
None of the animals could form any idea as to what this meant.
However, we as readers know it means that the pigs have been changing the wording of the commandments.