Short answer: Montag visits the old professor Faber because he knows the man has books and reads; therefore, he hopes Faber can teach him to comprehend what he reads.
His meeting with Christine on his walk home from work has deeply affected Montag as he begins to question his existential condition, pondering what she has said about people not really talking anymore in light of his relationship with his wife. Montag is further affected by his experience in the home of the woman with hundreds of books:
She made the empty rooms roar with accusation and shake down a fine dust of guilt that was sucked in their nostrils as they plunged about....
When a book falls, Montag's hand closes on it "with wild devotion, with an insanity of mindlessness to his chest." Then, when he goes home, he feels alienated from Mildred, feeling as though he is someone else's house. He tries to read to Mildred, but she cannot understand anything, saying, "Books aren't people. You read and I look all around, but there isn't anybody!" Montag himself reads a page ten times without understanding. He wonders where he can find a teacher; suddenly, he recalls having seen and old man in a black suit who hid something quickly in his coat pocket on a bench in a green park a year ago. When he sat by this man, they talked; Montag knew he had a book, but he said nothing. The older man gave Montag his address.
Montag takes the subway to Faber's house; when he shows Faber the Bible, the old professor says, "It's been a long time." Then he asks Montag why he has come to him. "I want you to teach me to understand what I read." He tells Faber something is missing in his life and he hopes that books will help him.