There are three different types of irony: dramatic irony, situational irony, and verbal irony. All types of irony are a contrast between what's literally expected and what actually happens. Dramatic irony is achieved when the audience or reader understands more about what is happening as a result of the action than a character understands at the time (Kansas State University, "Critical Concepts: Dramatic Irony"). Situational irony is achieved when the audience is led to believe something else will happen as a result of a situation than what actually happens ("Critical Concepts: Situational Irony"). Verbal irony is the most common and can also be called either sarcasm or facetiousness. Verbal irony is achieved when a person says something that literally means one thing but the speaker means to imply the exact opposite. Dr. Baker of Kansas State University gives us the example of a mother saying to her son in reference to his television viewing, "When you're finished with your serious studies there [television viewing], maybe we could take some time out for recreation and do a little math" ("Critical Concepts: Verbal Irony").
We can certainly see all uses of irony throughout Jane Austen's novel Pride and Prejudice. One example of verbal irony can actually be seen in the very first sentence of the book: "It is a truth universally acknowledged, that a single man in possession of a good fortune must be in want of a wife." We can clearly hear the facetiousness, meaning non-literal and humorous tone, in the sentence because it is certainly not true that a man wants to marry simply because he has a fortune; therefore, it is certainly not a "truth universally acknowledged." Austen particularly uses hyperbole, meaning exaggeration, to build the verbal irony expressed in this sentence.
We can see dramatic irony created as the relationship between Mr. Darcy and Elizabeth begins to develop. There are several moments early in the novel in which it is very clear to the reader Mr. Darcy is beginning to feel attracted to Elizabeth, such as when he comments on her "fine eyes"; yet Elizabeth sees all of his remarks to her as being antagonistic. Hence, Darcy's proposal comes as a surprise to Elizabeth, but the reader isn't at all surprised.