With its sarcastic undertones, the opening sentence of Pride and Prejudice is an example of verbal irony:
It is a truth universally acknowledged, that a single man in possession of a good fortune, must be in want of a wife.
This statement is ironic because, while the narrator claims to believe that all single men with wealth seek out wives, the rest of the novel is about all the ways that single women are the ones actively hoping to marry wealthy men (exemplified best in the Bennet sisters, but also by Charlotte, Caroline Bingley, and others).
In fact, in just the next paragraph, the narrator suggests that, when single wealthy men first set foot in a town, they are quickly “considered the rightful property" of the local women, who set their sights on marriageable men and become quite territorial about them. The implication, then, is that men aren't actually the ones desperately "in want of" a spouse; the truth that should be "universally acknowledge," then, is that many women are eager to marry wealthy men, not the other way around. This irony establishes that the narrator is critical of certain widely-held narratives and assumptions about marriage. It also sets the novel up to be more focused on the agency and stories of the women in the book than on the men.
While staying at Netherfield to take care of a sick Jane, Elizabeth spends more time with Darcy and witnesses more of his prideful behavior firsthand. In an example of verbal irony, Elizabeth states the following to Caroline Bingley in front of Darcy:
“I am perfectly convinced by it that Mr. Darcy has no defect. He owns it himself without disguise.”
This statement is ironic because Elizabeth clearly does not believe Darcy "has no defect." She is using sarcasm to make it clear that she believes the opposite—that Darcy is overly prideful and should be willing to own up to his flaws. Darcy, recognizing her sarcasm and feeling embarrassed, responds that he does have flaws, including his temper and inability to forgive people who have hurt him.
This moment highlights the ways that Elizabeth and Darcy provoke each other, each (at this point) unwilling to let go of prejudices they have of the other. As the two of them come to develop romantic feelings for each other later in the novel and move toward marriage, these moments of biting verbal irony decrease in frequency.
As one of the most heavily satirized characters in Pride and Prejudice, Collins—who has very little self-awareness—is easy for other characters to mock. While having dinner with Collins and the rest of the family, Mr. Bennet uses verbal irony to tease Collins about his obsession with complimenting his patron, Lady Catherine de Bourgh:
“You judge very properly,” said Mr. Bennet, “and it is happy for you that you possess the talent of flattering with delicacy. May I ask whether these pleasing attentions proceed from the impulse of the moment, or are the result of previous study?”
Through his subtle use of sarcasm, Mr. Bennet makes it clear (at least to his more self-aware family members) that he does not think Collins is gifted at “flattering with delicacy,” and he is not interested in Collins’s answer to the question. He is, instead, hoping to highlight the absurd way in which Collins has recounted for them the various compliments he has shared with Lady Catherine.
This is confirmed in the following paragraphs when the narrator states:
[Mr. Bennet’s] cousin was as absurd as he had hoped, and he listened to him with the keenest enjoyment, maintaining at the same time the most resolute composure of countenance.
In other words, Mr. Bennet is trying not to laugh at Mr. Collins’s lack of manners and inexplicable pride while gently teasing him.