The most important rule of the future society is that books are banned, with no exceptions. Literature in any form is seen as subversive, since it allows the formation of many differing opinions, and so firemen enforce the book-ban by rooting out and burning books and sometimes people. This ban shows the power of the government; no person is safe from informants and no opinions are allowed unless they are state-approved.
Another rule is that people shouldn't walk; they should take the subway or drive on the enormous freeways. Clarisse's uncle was once arrested for being a pedestrian; aside from the danger of being hit by the disaffected, uncaring drivers, walking instead of driving indicates a willingness to go against accepted convention.
One rule that is not stated outright, but is accepted by all citizens, is that they should be connected to the state television and radio broadcasts at all times. Montag experiences this when he tries to read in the subway and is distracted by constant advertising:
The people whose mouths had been faintly twitching the words Dentifrice Dentifrice Dentifrice. The train radio vomited... a great ton-load of music made of tin, copper, silver, chromium, and brass. The people were pounded into submission; they did not run, there was no place to run...
(Bradbury, Fahrenheit 451, Google Books)
This allows the government to continually distract the citizens from worrying about the real state of their country and the impending war; if the citizens are contented with shallow programming, there is little worry about individual thinking.