Man vs. Self: Montag is experiencing inner turmoil. The night that the firemen go and burn the house of the unidentified woman, Montag watches her burn with her books. He suddenly realizes that "There must be something in books, things we can't imagine to make a woman stay in a burning house, there must be something there. You don't stay for nothing" (pg 51). Afterward, when he is talking with Mildred about it, she could care less and demands that he leave her alone. He replies, " That's all very well, but how can I leave myself alone? ...We need to be really bothered once in a while. How long is it since you were really bothered? About something important, about something real" (pg 52). Later when he is talking with Faber, Faber tells him he did what he had to do and that it had been coming on for a long time. Montag agrees and says "I went around doing one thing and feeling another. God , it was all there. It's a wonder it didn't show on me, like fat." (pg 131)
Man vs. Man: Basically this can be narrowed down to Montag vs. Beatty. Beatty needles him constantly. When Montag returns to the fire station after feigning his illness, Beatty unmercifully browbeats him with quotes from famous books. "Montag's head whirled sickeningly. He felt beaten unmercifully on brow, eyes, nose, lips, chin, on shoulders, on upflailing arms. He wanted to yell 'No! Shut up, you're confusing things, stop it" (pg 107) All the time Beatty is doing this, he is planning on burning Montag's house that night. When he does, he taunts Montag again "Didn't I hint enough when I sent the Hound around your place?"(pg 113) Even when Montag grabs the flame thrower and aims it at Beatty, Beatty taunts him. He calls him "a second-hand litterateur" and a "snob" (pg 119) He dares him to pull the trigger, and Montag does. Then the race is on and it is man vs. man when he is trying to escape. They are hunting him with helicopters, men on foot, and a Hound that has been brought from another district.
The pages listed are in my edition, an old one. They may not be exactly the page numbers in your book, but they will be in the vicinity.