Irony is a literary device in which there is a contrast between what is said or done, and what is meant.  Verbal irony is when what is spoken is not meant to be taken literally, or in the case of sarcasm, the meaning is exactly the opposite of what is said.  Situational irony is when what is expected to happen (what would be typical or ordinary) does not happen, or when what happens is completely unexpected.  Dramatic irony is when the audience (or reader) knows something the characters do not know.

To Kill a Mockingbird is full of all three types of irony.  As a narrator, Scout often includes verbal irony in a story of situational irony.  The account of her first day of school in Chapter 2 is a great place to look.  First, it is ironic (situational irony) that the students in the class know more than their teacher, Miss Caroline.  When Scout attempts to politely educate Miss Caroline on Walter Cunningham, for example, it is ironic that Miss Caroline becomes offended and ends up punishing Scout.  Scout's intentions are pure.  So pure, in fact, that she is not even aware that she is offending her teacher, and neither is the class.  When she says, "Walter hasn't got a quarter at home to bring you and you can't use any stovewood," Miss Caroline believes Scout is being rude and probably verbally ironic (or sarcastic), but in fact, she is genuinely concerned and being as polite as possible.