Generally speaking there are three common kinds of irony: verbal irony, situational irony and dramatic irony. All kinds of irony rely on multiple meanings.
Verbal irony occurs when a word or phrase has at least two meanings - one overt and direct and the other in contrast to the overt and/or denotative meaning. Sarcasm is often used as an example of verbal irony.
Another kind of a example would be if in a plane landing where the pilot was shaking for some reason and this shaking led to a dangerous and risky landing, the co-pilot says after the landing, "That was shaky for a bit there." This is ironic because shaky has two meanings - one relating to the pilot's shaking and the other to the danger of the landing.
Situational irony occurs when a highly unlikely or opposite to expectations happens. This might loosely be described as a "twist of fate" and might be exemplified by a person who has just quit her job as a driver's education instructor and when walking home is struck by the car of a former student.
The irony here is that the instructor's job was to teach safe driving but she is injured by a dangerous driver.
Dramatic irony occurs when the audience (and a character or characters) is aware of some information that other figures in the story are not aware of. This technique is used in literature, film and theater.
Horror and suspense films often use this technique when the audience is shown that someone or something dangerous is on one side of a door and a character in the film stands on the other side of the door, unaware of this danger. The scene has two meanings - one for the informed audience and another derived from our identification with the uninformed character.