From the very first pages the narrator's delight in making ironic, witty comments about her chararcters is clear. Frequently these come through the mouthpiece of Lizzy Bennet, but they also are common occurences from the omniscient narrator. To give just one example, Lizzy Bennet employs a rather cruel form of irony to describe Miss De Bourgh on her first meeting:
"I like her appearance. She looks sickly and cross. Yes, she will do very well for him."
In this example of irony we need to possess knowledge about matters exterior to the context in order to detect and fully appreciate the irony. Here, obviously Lizzy does not like the appearance of Miss De Bourgh - her "liking" is only based on her dislike of Mr Darcy and his and Miss De Bourgh's intended union. Such use of verbal irony, or saying the opposite of what is really meant, is used throughout this novel, but the reader must be aware of the wider context in order to detect and enjoy the uses of irony.
Irony definitely extends beyond the verbal in this novel however. It is highly ironic that Mr. Darcy, having just persuaded Mr. Bingley to abandon his pursuit of Jane Bennet, then goes on to propose to Lizzie Bennet, in spite of exactly all of the same objections standing against such a union. Likewise, Lady Catherine's visit to Lizzie Bennet to try and prevent the union of Darcy and Elizabeth, unknowingly and highly ironically, is a key event that brings her nephew and Lizzie Bennet together.
That is enough to get you started - you might also want to think about the kind of irony employed by various characters, and indeed, the narrator herself. Linked to this you will want to examine the characters irony is used against and their awareness - or not - of the irony that is employed against them. For example, Mr. Bennet frequently employs irony against his wife and also Mr. Collins, who are blissfully unaware of the double meaning.