In your thinking about this question, you would do well to compare this novel to another similar dystopian novel, such as 1984, Brave New World or A Handmaid's Tale. Reading and comparing Fahrenheit 451 with any of these novels would give you a much better idea of dystopian fiction and some of the central components of dystopia.
However, just to give you a few ideas, I would pick the following three elements:
Censorship: clearly, in this novel, the banning of books and the censorship of knowledge is a central theme. The government of this world have decided to ban all books and burn them for reasons that are not explicitly spelled out. However, this could easily be compared to the workings of the Ministry of Truth (irony there) in 1984.
Simulated experiences: another key element is the rise in popularity of simulated experiences instead of reality. This is most clearly seen in Mildred and her "family" and her devotion to the screens that her friends come and enjoy together. The description of what these screens show is a maelstrom of different images and experiences:
Abruptly the room took off on a rocket flight into the clouds, it plunged into a lime-green sea where blue fish ate red and yellow fish. A minute later, Three White Cartoon Clowns chopped off each other's limbs to the accompaniment of immense incoming tides of laughter. Two minutes more and the room whipped out of town to the jet cars wildly circling an arena, bashing and backing up and bashing each other again. Montag saw a number of bodies fly in the air.
Such disrupted and fast-changing images and the avidity with which Millie and her friends watch them show how they are living more in a simulated reality than in reality itself, a point driven home when Montag forces them to listen to "Dover Beach" and they start crying. This is a world that has truly embraced the mass media and forsaken individual thought and expression.
Alienation and loneliness: Montag is above all a lonely man. He, throughout the course of the novel, realises how shallow his society and life and marriage has become and yearns for companionship and ideas, which he finds in his friendship with Clarisse and then in books. Again, this is a key theme for 1984 with the central protagonist realising how alone he is in his world and seeking companionship as an act of defiance against his world.