Loneliness can clearly be seen in Montag's character as he encounters other characters. In his exchanges with Clarisse McClellan, his eyes are opened to how lonely he is as she asks him how happy he is. As he goes home and feels completely empty in his relationship with Mildred, his wife, he begins to understand the relevance of the question. For Montag, this may be when he starts to actually realize that he is indeed lonely. Later Clarisse tries to paint him as if he is not in love. This offends him because he does not want to think he is lonely. He wants to believe he is in love with his wife. But a look at his relationship when he goes home that day reveals to him that neither of them (Mildred or Montag) know exactly how they met. Obviously their relationship is shallow.
Clarisse's family talks. Montag watches and understands that this happens. This habit reveals to him that he does not have that rapport with other people. This reveals both loneliness and alienation.
Alienation occurs for Clarisse as she is removed from the other students to have regular visits with the psychiatrist in order to figure out what's wrong with her.
Alienation occurs for Montag as he is singled out slowly and separated from the other firemen. First, the Mechanical Hound begins to notice Montag. Then, he's not as interested in the games the other men play. Finally, they go on a call ending at Montag's house and he is completely alienated from the other men.