Montag does not actually die within the pages of Fahrenheit 451. At the end, he has joined a new society of "book people," who live in the woods. His death is staged, however, by his old society. The mechanical dog attacks a man walking on the street, which is aired on live tv. They say that the man is Montag, so that all the viewers believe they are safe.
The way the attack is presented does seem normal. The people blindly accept whatever is fed to them, so they believe Montag is bad and that his death is good. It does not seem that they even question whether murder itself is wrong.
In the future world of Fahrenheit 451 suicide was not uncommon (or at least, suicide attempts were not uncommon) and the death of someone was not looked upon in the same manner as it is now. When the technicians come to pump out Mildred's stomach after she overdoses, one casually remarks that the reason they come on these types of calls rather than doctors is because they get 9 or 10 cases a night. When Clarisse talks to Montag, she tells him about how she is afraid of people her own age. She says that so many of them hurt one another and that 6 of her friends have been shot in the past year. There is clearly little regard for life. People live for the moment and for pleasure. The society of Fahrenheit 451 is geared for pleasure. When Beatty explains to Montag why things are the way they are, he tells Montag that if the people are kept happy and busy with mindless activities then the people just follow along like sheep and they don't bother to think. This is how the government in the futuristic society of the book controls people. Furthermore, Beatty says that five minutes after a person dies, "...he's on his way to the Big Flue,...". Five minutes is all that is given for time to grieve for a lost loved one.
He doesnt die. adleast not in the book.