Censorship is shown through the books that they burn. People aren't allowed to read books, and that is the most extreme form of censorship that exists. Not only this, but people talking is looked down upon; Clarisse mentions the fact that her family talks together quite a bit, and how that is extremely rare. In the schools, the kids are fed censorshipped and watered-down versions of reality, in order to keep them feeling like they are full of facts, when in fact they are not. So that is another form of censorship in the novel.
Their society got to this point because people didn't want to read an entire book in order to know what it was about; so, books got shorter and shorter until they were just a line or two of plot summary. Then, books often contained information that offended people and made them unhappy. So, to please the masses, the books were censored; anything offensive or depressing were taken out. Pretty soon, reading at all was a dying art, and looked down upon, and it wasn't long after that that books were forbidden and the entire fireman scheme was undertaken.
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