Fahrenheit 451 is mostly written from a third-person point of view. However, there are moments when Montag interrupts this style and speaks from the first-person point of view. Bradbury makes the transition from third person to first very subtly. The only indication is when the pronoun shifts from "he" to "I." Apostrophe is a first-person point of view when the speaker addresses an absent person, idea, or even himself.
The most significant (and perhaps the only) times this occurs is at the beginning and at the end of the novel. Only six pages into the novel (my page 9), just after Montag's first meeting with Clarisse, the narration shifts to Montag's inner monologue (and this is apostrophe):
Of course I'm happy. What does she think? I'm not? (9).
There are also moments when the narration is partly third-person and part first person. On the next page, still thinking about Clarisse, the narration goes, "Why, he thought, now that I think of it, she almost seemed to be waiting for me there, in the street, so late at night . . . " (10). This is not strictly considered apostrophe, but I include it to show the subtle way the narration can shift from third-person to first.
About five pages from the end, Montag tries to remember Ecclesiastes and Revelation following the meeting when Granger tells him he is the book of Ecclesiastes after Harris. "What is it? Yes, yes, part of Ecclesiastes. Part of Ecclesiastes and Revelation. Part of that book, part of it, quick now, quick, before it gets away, before the shock wears off, before the wind dies" (143). Had this been third person narration, it would have been something like "Montag struggled to recall the books of the Bible . . . " Instead, we are given Montag's inner monologue to reflect his state of mind first hand and also to reinforce the idea that he is thinking for himself, a quest he began when Clarisse taught him to question things.