What are some laws in the society of Fahrenheit 451?
The most important law is the one that bans books. Without books to inform differences in opinion, people are primed to accept anything the government tells them is true. The firemen, like Montag, are allowed to burn books and burn people when they resist; the law allows them to be judge, jury, and executioner, without any other due process. This law informs the entire book and its themes, although Bradbury based his initial work on the alienation of society through television.
Other laws are hinted at through conversations and context: younger men are required to work at some job -- Montag is a firemen, the husband of his wife's friend is a soldier -- while previously retired persons like Faber are mostly ignored. Realizing that he has been pigeonholed into a profession, Montag says:
"Was I given a choice? My grandfather and father were firemen. In my sleep, I ran after them.
(Bradbury, Fahrenheit 451, Google Books)
Walking on the side of the road is discouraged, since new laws allow cars to drive one hundred miles-per-hour. Due process seems to have been eliminated, as the firemen have permission to kill people when they break the law. In every respect, this is a society of drasticly reduced personal freedom, and a world where the individual is subservient to the state.