Montag met Faber in a park a year before the story started.
The first time Montag mentions Faber, it is very brief. He does not say who Faber is or what happened during the encounter that made it so memorable.
What a strange meeting on a strange night. He remembered nothing like it save one afternoon a year ago when he had met an old man in the park and they had talked... (Part I, p. 8)
This is very early in the book, so at this point the reader has no idea what Montag is talking about. He remembers the encounter with Faber when he is thinking about Clarisse. He clearly associates the two because both of them make him question himself, his profession, and his society.
We learn later that Montag saw Faber in the park, and also saw him quickly hide something. Montag stopped to talk to him, and eventually Faber let his guard down and they had a conversation.
The old man admitted to being a retired English professor who had been thrown out upon the world forty years ago when the last liberal arts college shut for lack of students and patronage. His name was Faber, and when he finally lost his fear of Montag, he talked in a cadenced voice, looking at the sky and the trees and the green park... (Part I, p. 70)
The meeting ends with Faber quoting “a rhymeless poem.” Faber tells him that he talks “the meaning of things” and is alive. The meeting clearly made an impression on Montag. When he finally got up the nerve to look Faber up in order to further explore the world of books, Montag knew he was in very deep. Montag seeks him out because he himself can steal books, but is not really educated enough to read them.
Please note that editions of books vary. These page numbers are from the 2011 edition (ISBN 9781439142677).