The characters in Fahrenheit 451 are directly related to the plot in that they are all products of their environment. Since the plot relates to themes of censorship, isolation, and oppression, each character reacts in a different way. Montag is initially happy with his role as a fireman, but some part of him is dissatisfied, expressing his unconscious by stealing books. Mildred is entirely satisfied with her life as a willing pawn of the government system, and she has no wish to change anything, except perhaps to immerse herself even further into the isolation of television. Chief Beatty is an interesting combination of Montag and Mildred; he believes passionately in the causes of the government, that books are inherently harmful to the human psyche, but at the same time he seems to have read extensively and uses quotes and ideas from great writers to manipulate others.
The character most affected by the plot is Montag, as he changes his entire worldview during the course of the book, but his changes are triggered by his meeting with Clarisse:
"You're not like the others... When I said something about the moon, you looked at the moon, last night. The others would never do that. The others would walk off and leave me talking. Or threaten me. No one has time any more for anyone else. You're one of the few who put up with me. That's why I think it's so strange you're a fireman, it just doesn't seem right for you, somehow."
(Bradbury, Fahrenheit 451, Google Books)
Each of their meetings brings out something unusual in Montag, until she disappears; Montag had felt that something in his life was missing, and until Clarisse entered it and then left, he wasn't aware exactly what it was. The plot, then, shows each character as a facet of their environment, and as events move forward, the characters react as they have been trained to: Beatty tries to keep order, Mildred withdraws, Clarisse is destroyed. Only Montag pushes through events and becomes a different person, because he has discovered his individuality and is empowered by it.