From his conversations with Clarisse, Guy Montag learns to question things. He learns to reflect on what he thinks and does. Prior to this point in his life, Montag was quite passive. Above all, he learned to think about the personal and social implications of his actions.
The most obvious thing Montag learns is that his career as a book burner has been culturally and personally counter-productive. He had been destroying things that could have (mentally) set him free.
Another lesson he learns, although it is a philosophical cliche, is to consider whyhe (and others) lives the way he does. This was the problem for the passive people in Montag's society. Mildred is another good example. She never questioned why she was so engaged with the shows on her parlour walls. She never questioned the work of the fireman. Even when Montag, her own husband, tried to open her mind, she was in such denial, she could not bridge the question: why.