In Fahrenheit 451, Bradbury does not reveal where and when Montag stole his first book. Early in the book, he hints at Montag's stolen book collection at several points, like when the Mechanical Hound growls at him in the firehouse:

"If someone here in the firehouse knew about the ventilator then mightn't they "tell" the Hound . . . ?"

After Captain Beatty visits his house, Montag finally unveils his collection to his very shocked wife, Mildred. In total, Montag takes "some twenty books" from behind the grille before apologising to Mildred and then asking her to read them with him.

So, when Montag steals a book from the lady whose house he burns, it is not the first time. By not revealing when and where he first stole a book, Bradbury implies that Montag has been dissatisfied with the status quo for some time but needs a little encouragement. This is why his meeting with Clarisse is so significant. 

In Fahrenheit 451, where did Montag hide his books after the ladies left?

In Part II of Ray Bradbury’s novel Fahrenheit 451, Guy Montag recklessly reads banned poetry to his wife’s friends. While Faber listens to the conversation through an earpiece, Montag spiritedly shows Mildred’s friends his forbidden collection of books and begins to read poetry. When Faber urgently raises the obvious dangers of such a move, Montag barks that he wants to,

Scare hell out of them, that's what, scare the living daylights out!

Montag’s reading of “Dover Beach” seems to have the opposite effect. Mrs. Phelps, Mrs. Bowles, and Mildred all react with tears of anger and pain. The women seem to feel genuine anguish as they experience emotions brought on by the reading of the poetry. They depart flustered and it seems obvious that they plan to report Montag to the authorities. Mildred tosses some of Montag’s books in the incinerator.

Knowing his position is tenuous, Montag rushes to collect and retrieve his books. He finds them hidden all around the house and a particularly large stack “behind the refrigerator.” Montag then,

…carried the books into the backyard and hid them in the bushes near the alley fence. For tonight only, he thought, in case she decides to do any more burning.

Montag’s home is burned by the fireman later that night and the books are lost.

Montag, a fireman charged with the responsibility of burning books, was convicted by Clarisse’s probing to question the purpose of his job. In his quest to learn more about what books contain and establish the genesis of book burning, he stole several books the first of which he hid under his pillow as he and Mildred slept on separate beds. Afterwards, he hid the rest of the collection in the ventilator grill. One day Mildred’s friends come over to Montag’s house to chat and watch their usual shows and Montag, angered by their superficiality, switches off the walls and reads them poetry by Mathew Arnold. This angers and saddens them and they are forced to leave. After this Montag realizes he has made a mistake and goes for his book collection in the ventilator grill and "He carried the books into the backyard and hid them in the bushes near the alley fence."

Where does Montag hide his book in Fahrenheit 451?

Guy Montag's curiosity about books and why they must be burned begins before the opening of the story. Even though he thought "[It] was a pleasure to burn," he collected nearly 20 books and hid them in the grille of the air-conditioning system of his house. The final book he stole was from a fire where he watched a woman die with her books. He knew there had to be something of value in them, so he determined to read the ones he had collected.

Before Montag had an opportunity to read the most recent "theft," Beatty came for a visit. Montag stashed the book under the pillow he was using while he recovered from being ill. The book stayed there during a long monologue from Captain Beatty, where the history and rationale of book burning was a central theme.