Guy Montag goes from a character who is complacent and who thinks that he is happy; in fact, he loves his job and is supremely confident in what he does. He is a man who feels, as the first line of the novel states, "It was a pleasure to burn," who, for his entire life, had lived and gone along with everything, and felt happy about it. In fact, "for as long as he remembered" he had had a smile on his face.
He starts to change upon his first meeting with Clarisse. She asks him if he was happy, and he asserts defensively, "Happy! Of all nonsense!" not ever having asked himself that question before. But she was truly happy, a peaceful happy that lent her an inward glow, so, when he steps into his cold house and discovers his wife's suicide attempt, he wonders if he really IS happy. He can't help but compare Clarisse's inner light to Mildred's inner misery. He wonders what has made both of them the way that they are.
His continued visits with Clarisse impact him even more; he wonders if books, being forbidden, are at the center of what is wrong with his society. The real changing point for him comes after he torches Mrs. Blake's house, and she chooses to go down with her books and home. This affirms for him that there is something vitally important in books, and something seriously wrong in his society. He is so disturbed he becomes sick, and after Beatty's visit decides to hunt answers in books. However, he has a hard time, so, enter Faber. Faber teaches him why books are important, and Montag is so fired up about it that he is willing to undermine the entire system to give books a chance.
At this point, he has changed from an accepting civilian to a questioning independent thinker. He is disillusioned with his world; he is unhappy and seeking answers; he is willing to fight to get answers and to enact changes in his society. He challenges Mildred's mindless friends, and in the end, gains so much confidence in the trail that he is seeking that he has the strength to torch Beatty and go on the run.
At the end of the novel, he is a man on the run, wanted, hunted down, who has rejected the entire premise of his society. No longer is his happiness dictated by his society; he goes off on his own to find what real happiness is. With Granger, he is willing to rebuild society, to undertake the task of "remembering" what real happiness is.
I hope that these thoughts help; I provided some links below that you might find useful also.