Irony is typically difficult to clearly explain, especially as a literary device, since part of the point of its use is to be unclear. According to the famous definition of irony given by Henry Watson Fowler in “The King’s English,” irony occurs when “...the surface meaning and the underlying meaning of what is said are not the same.” Irony can be a powerful literary tool and is typically classified into three distinct types. Once you understand which type you are working with, you'll better be able to discuss it as you write your essay.
Irony often expresses itself within a character's speech. For example, if a protagonist claims to be afraid in one context but reveals fearlessness in another, then he is using verbal irony. In the case of Plato's dialogue "Phaedo," Socrates claims to have no knowledge at all, famously pretending to be ignorant. However, it becomes clear that he actually knows many things and is depicted as philosophically superior to other characters.
Verbal irony is defined by the contradiction between what a character says and what that character means. However, dramatic irony occurs when a character has one understanding of the situation he finds himself in and the reader (or audience) another. For example, the reader of Shakespeare's "Much Ado about Nothing" knows that Hero was always faithful to her soon-to-be-husband, Claudio. Claudio, however, does not know this and acts as if the opposite is true.
The most exaggerated form of irony is situational. This occurs when neither the audience nor the characters are endowed with any special knowledge about what is about to happen. Everyone expects one set of circumstances and is, instead, confronted by another. This can be used for comedic effect but is more typically associated with tragedy. Alfred Hitchcock used situational irony in his suspenseful movies: He was notorious for shocking audiences with wildly unpredictable conclusions.
Once you've identified a particular type of irony, provide an account of the literary effect it was intended to produce. Keep in mind that any type of irony could be used by an author for a variety of purposes. For example, Jonathan Swift was able to harshly criticize English monarchy in "Gulliver's Travels" without fear of punishment as he used ironic humor to mask his judgments. Quote the ironic passages, pointing out what the author is actually saying.
As you're writing, assess whether the use of irony is successful. Irony shouldn’t be immediately obvious, but it also doesn't serve a purpose if it is undetectable. Review whether the author’s use of irony adequately fulfills the purpose that inspired it. If the intent is to gently teach the reader a lesson, evaluate if this is done well or whether the irony is used clumsily. This is the ultimate standard by which literary irony is to be judged when reviewing it.