I can try to list a few to get you started. When you are looking for ironies, look for anything that is the opposite of what you might expect. There are examples, obvious and more integrated, throughout the entire novel.
1. Firemen that burn books instead of put out fires.
2. The person to turn Montag into the authorities is his own wife.
3. Montag, a fireman, gets an alarm turned in on his own house, and it is torched.
4. Beatty, captain of the firemen, is extremely well-read and knowledgable about books, to the extent that he can quote them from heart.
5. Families that are stable, loving, and funtioning, are targeted as threats and destroyed in their society.
6. Montag and Mildred can't remember where they met.
Those are just a few ideas for you; I hope that helps a bit! Good luck!