The quote at the beginning of Fahrenheit 451 is:
If they give you ruled paper, write the other way.
--Juan Ramón Jiménez
Jiménez was a Nobel-Prize-winning poet from Spain, and his poetry is still read and taught today. This quote speaks to the anti-establishment way of thinking, the innate opposition to rules and regulations that informs much of the Libertarian ideal. In this case, because of the enormous power taken by government in the book, the quote represents a direct opposition to instructions; ruled paper is meant to constrain lines of text, ostensibly for clarity of composition and reading, but Jiménez entreats the reader to make their own rules and "write the other way," outside the lines, vertically, whatever creates the best outcome. It does not necessarily mean deliberate law- or rule-breaking, but simply to move beyond the constraints of rules to express personal creativity. It's significance to the novel is simple: Montag, whose entire life has been spent "inside the lines," starts to make personal decisions and "write the other way" in his personal life; his eventual epiphanies and escape come from breaking the rules, not from following them.