How did Montag finally get Faber to consider really helping him?

As an intellectual outcast from society, Faber is primarily a thinker, not a doer. He's deeply pessimistic about the prospects of overthrowing the regime. This fits in with his generally grim view of human nature; he doesn't think much of the revolutionary potential of the masses who've effectively been tranquilized by the state. Faber sees the value of Montag's plan to destroy the regime from within by hiding books in firemen's homes, thus sowing distrust among those charged with implementing the state's book-burning policy. But he's not prepared to go along because the plan, though ingenious, is too dangerous and he's simply unwilling to risk his own neck.
Montag persuades Faber to go along with his plan by tearing pages out of a Bible, a particularly rare and precious book in this society. He knows that this will get Faber's attention, as he won't want Montag to destroy the whole book. Faber gets the message, and reluctantly agrees to help Montag, giving him a two-way communication device called a green bullet which will allow them to stay in touch at a distance.

Montag initially met Faber in the park apparently hiding something. In Part 2, he thinks Faber might help and goes to find him.
At first Faber is dubious and perhaps suspicious, saying it would be a waste of time. War and destruction are inevitable, with the following cycle of restoring society.
Faber thinks books will be of limited use to change all that, but Montag has an idea. He thinks they could turn the tables, making it look like the firemen are keeping books in their houses. Turning them in would take them out of duty, and ultimately society will implode.
Faber realizes that Montag is willing to risk everything, so he agrees to help, even figuring out how to get enough books to make the plan work.