The two most common types of irony are situational irony and dramatic irony. In situational irony, both the character/characters and audience are unaware of the true situation: the outcome of events do not match expectations. Here are examples of situational irony.
Dramatic irony occurs when the audience knows facts about the character (or specific clues of the story) that the character is not privy to. (Please refer to the link for examples of dramatic irony).
In Chapter 5 of The Scarlet Pimpernel, a good example of dramatic irony is the moment the Comtesse forbids her daughter, Suzanne, to speak to Lady Marguerite Blakeney.
"Suzanne, I forbid you to speak to that woman," said the Comtesse, sternly...She had spoken in English so that all might hear and understand;... As for Lord Antony and Sir Andrew Ffoulkes, their very hearts seemed to stand still with horror at this gratuitous insult... instinctively both glanced hurriedly towards the door, whence a slow, drawly, not unpleasant voice had already been heard.
"We are in England, now Madame," rejoined the Comtesse coldly, "and I am at liberty to forbid my daughter to touch your hand in friendship. Come, Suzanne."
The dramatic irony is that the Comtesse and all her family owe their liberty to the Scarlet Pimpernel, who is the alter-ego of Sir Percy Blakeney, Lady Blakeney's husband. In the story, it is the Scarlet Pimpernel who continues to be responsible for the daring escapades of various aristocratic families from the Guillotine. As such, the Comtesses' insult is ironic: she does not know that she is insulting the wife of the man responsible for her own rescue.
Another irony is that Lady Blakeney herself does not yet know her own husband is the Scarlet Pimpernel, the man (along with his courageous band of followers) responsible for rescuing the Comtesse's family from the blood-thirsty clutches of Madame La Guillotine.