EXPOSITION: Readers meet Montag, a fireman whose purpose is to create fire that burns books; Mildred, his wife who prefers her seashells and 'the family' (TV) to real people; Clarisse, a curious girl who remains counter-cultural in beliefs and purpose; and Captain Beatty, Montag's boss who helps perpetuate the dystopian idea that thought is destructive and people are better suited when they are ignorant. This society seems backwards to modern society... or is it?
INCITING INCIDENT: Montag watches a woman commit suicide by going into a house filled with kerosene. She lights the match herself because books are so valuable to her.
RISING ACTION: Montag explores free thought. This occurs as he gets sick and wants to quit, as he tries to get Mildred to buy in to the cause, and as he begins pursuing Professor Faber. Throughout this time, the Mechanical Hound begins to sense something changing in Montag's DNA. Faber and Montag create plans. Mildred leaves Montag. The Mechanical Hound discovers Montag at a fire when Beatty is killed by Montag. Montag seeks Faber again. A chase begins.
CLIMAX: During the chase, Montag has moments of feeling the Hound will overtake him. Eventually, Montag watching other peoples' televisions realizes that the Mechanical Hound is now after someone else. This comes as a result of Montag using the river and alcohol to mask his chemical scent.
FALLING ACTION: Montag follows the directions given to him by Faber and finds a band of men devoted to the same cause: preserving the truth of books.
RESOLUTION: Although the society isn't changed, Montag's circumstances are and he finds new, but meaningful purpose.
For a more detailed set of events, you will need to reference the summaries enotes provides. I have linked some below.