They walked still further, and the girl said, 'Is it true that long ago, firemen put out fires instead of going to start them?'
'No. Houses have always been fireproof, take my word for it.'"
Guy Montag is a fireman.  In a society where books are forgotten and houses are fireproof, fireman start fires, burning the collections of those few who preserve them, clinging to old ways.   As Captain Beatty, the Fire Chief says, fire is clean, quick and sure; and what's the value in musty old books about people that never lived?
But, one day Montag runs into Clarisse McClellan, a bright and inquisitive seventeen-year old.  Clarisse questions the society in which they live, and she immediately befriends Montag.  “Are you happy?” she asks.
Montag insists to himself that he is happy as he arrives home to find his wife, Mildred, unconscious from an overdose of sleeping pills.  As he watches the technicians perform their seventh stomach pump of the night, he realizes that Mildred is a stranger to him, he can’t even remember where the two first met.
The next day, the call takes them to an old woman whose attic is full of books, the woman shocks him by choosing to be burned alive along with her books.  Montag's dissatisfaction with his life increases, and he begins to search for a solution in a stash of books that he has stolen and seeks help from Faber, a former English professor and old acquaintance.  He gains the man’s trust, and together they plan to undermine the entire system of firemen.
Soon after, Montag and his fire crew pull up in front of his own house. 
Fahrenheit 451 is bold indictment of censorship.  There is no symbol of repression more powerful than the burning of books.  What’s frightening is how little would have to change for our society to resemble that of Montag’s.  The citizens in the story are not evil, they are simply short sighted.  They believe what they are told, never thinking to question.  They like their TV, and their television has shaped them by becoming more exciting, and basically more content-free.  Cars are fast, life is easy and everyone is happy, at least they all think they are happy, sublimating their misery until it leaks out in “accidental” suicide attempts.  Books are simply opposing progress and comfort.  Fahrenheit 451 serves as a warning that any society can forget the importance of ideas, succumbing to comfort without realizing what they are losing.
There was only one part, which I feel that I have to complain about.  During one passage, Montag is riding the subway with the Bible on his way to meet Faber.  There seemed to be two things going on at once, although I was not sure.  Even after reading it over and over, a total of four times, I still had no clue to what exactly was happening.  Eventually, I got frustrated, so I skipped over it and it luckily had nothing to do with the plot or I would have been lost
Fahrenheit 451 is a classic and is the type of book that will be read for many years to come. Although the text is the same in each edition, I highly recommend reading the Ballantine edition.  It contains an afterward and a coda, where Bradbury tells you in the first person what he thinks about his masterpiece and some of the things that have happened to him since publishing the book.
It's a quick read. You can easily go through its 179 pages in a couple sittings.  But the experience doesn't stop when you put the book down. Bradbury makes you think. And you'll keep thinking long after you've finished Fahrenheit 451.