Montag's desire to read books is a slow process that gradually builds to the actual act of reading one. At the beginning of the story, he already has a book hid in his house, because as he walks into the house the first time we meet him,
"he stood looking up at the ventilator grille in the hall and suddenly remembered that something lay hidden behind the grille."
He only looks up there after he pondered Clarisse's question of, "Are you happy?" So here, Bradbury seems to be alluding to the fact that Montag was not happy, and his unhappiness has led him to books; perhaps he feels that they hold the answer. His desire to read books is there even before the novel begins. However, Clarisse sparks his interest more, along with Mildred's suicided attempt. He realizes, through these two events, that he indeed is not happy, and neither is his wife, or most people that he knows, for that matter. But Clarisse is; she's happy, and perhaps books are the reason why.
While all of this is mulling around in his head, he is called to burn Mrs. Blake's house. Mrs. Blake, rather than leaving her books, chooses to be burnt alive with them. This really gets to Montag; he thinks that if someone is willing to die for books, then there HAS to be something in them, there just has to be. So, this adds to his interest. Then is the visit from Beatty, where he explains the entire history of firemen, and how books became unpopular. Then at the end of his lecture, he basically gives Montag permission to read: "We let the fireman keep the book twenty-four hours." Montag takes full advantage of that time-frame, and tries to read with Mildred. He lists all of the things wrong in the world, and tells Millie, "An hour, a day, two hours, with these books, and maybe..." thinking that somehow they hold the answer to life's miseries. It is a pretty futile process though, as Mildred complains the entire time and is upset that he isn't going to work. Frustrated with her and her friends, he seeks out Faber, who confirms everything he has been suspecting about books. From there on out, he has made his decision; books are worth fighting for, and he takes that conviction to the end of the book.
So, through a slow, gradual process, Montag goes from secretly hiding a book but never reading it, to wanting to read it, to openly reading it, to planning subterfuge in order to bring books back, then open rebellion in the name of books.
Montag is overcome by insatiable curiosity regarding the forbidden object.
Montag has several conversations with eccentric 17-year-old neighbor Clarisse who challenges his right to authority over others and also who questions his happiness. Montag begins to think about his station in life and about his feelings of happiness as related to his society. Montag wonders more about this feeling of unhappiness after Millie's suicide attempt and the cavalier manner in which the medical team take care of her mental state.
Montag is intrigued by the woman, Mrs Blake, who decides to burn herself along with her illegal library of books. Montag steals one of the books from the fire. Beatty comes to see him after he does not report to work and explains just what it is that firemen do to help society. He is told that he has 24 hours to satiate his curiosity before the firemen will burn the book for him.
He attempts to read to Millie which makes her extremely uncomfortable. But he is such a poor reader that the book makes little sense to him.
Montag is not sure just exactly what is in the books that is to be feared. Montag rejects the authoritarian control that the Firemen have on society. One of the quotes in the book states that not all men are born equal, but they are made equal through the society that does not allow discomfort caused by intelectualism or the discomfort caused by the confusion of different ideas presented in books.
Montag desires to read as a way to rebel against the authority of his society. Montag seeks out the help of Faber who is very suspicious of his desire to learn to read. Faber tells Montag that learning to read will only allow him to "nibble around the edges" and that society will crash from the pending war.
Montag finally rejects his society and runs away as a fugitive only to be embraced by a society of "living books".