What does Montag hope the books will tell him?

Montag hopes to find answers both to personal questions, such as those concerning happiness, and global concerns, such as reasons for war.
Toward the end of Part I, after the old woman chooses to die with her books, Montag wonders more about their content. He tells his wife, Mildred, that there must be things in books that they can’t imagine, and he describes what he thought about books:

for the first time I realized that a man was behind each one of those books. A man had to think them up.

Later, after he reveals his cache of books to Millie, he tells her his worries that they are on the verge of catastrophe and that the books might be the key to averting it, by helping them piece things together:

"We’ve got to start somewhere here, figuring out why we’re in such a mess."

In Part II, after Montag has started to read aloud to Millie, he ponders the state of global affairs, including other countries’ hatred of their own, as they play while others work. The books “just might stop us from making the same damn insane mistakes!” (emphasis in original).
After speaking with Faber on the telephone, Montag takes the Bible to his house, hoping that Faber can teach him to understand what he reads. He explains that he wants to learn why they are not happy:

Something's missing. I looked around. The only thing I positively knew was gone was the books I'd burned in ten or twelve years. So I thought books might help.

After analyzing his life, Montag realizes that he has a meaningless existence and attempts to find possible answers to life by reading literature. Montag believes that the content of books might possibly lead him in the right direction toward happiness and contentment. Unfortunately, Montag initially struggles to comprehend the information he is reading and asks Faber to show him what literature has to offer. Faber explains to Montag the significance of literature and guides him in gaining an understanding of how novels and books can positively influence a person's life. Essentially, Montag hopes to gain perspective and improve his life by pursuing knowledge and reading literature. Instead of destroying books and lives, Montag wishes to build, and he finds fulfillment in reading literature. By the end of the novel, Montag begins to memorize the Book of Ecclesiastes, which he will share with others when they begin to rebuild a literate society.