How does Holden, in The Catcher in The Rye, show alienation?

Holden Caulfield is the angst-ridden teenager in The Catcher in the Rye who struggles with both depression and isolation. He is deeply reflective and spends much of the space in the novel commenting on how the world around him is disappointing. Holden is caught between the world of children, which he finds predictable and full of imagination, and the world of adults, which seems confusing. He therefore clings to things like his hunting hat, which most people find odd. (He is once told, "Up home we wear a hat like that to shoot deer in . . . That's a deer shooting hat" [Chapter 3].) Holden recognizes that it sets him apart as quirky, but he holds on to it nonetheless, sometimes returning to it when the world seems especially confusing.
This sense of alienation leads him to feel disconnected from both realms, childhood and adulthood. In Chapter 9, he relates, "I was sort of crying. I don't know why. I put my red hunting hat on . . ." In effect, Holden often alienates himself as a means of coping with the world around him. He isn't quite sure how to relate to people, and when he tries, he is often met with disappointment. In his efforts to connect with Sally (who is definitely not his best match, as she lacks depth and sincerity), he launches into a discussion of how depressed he feels, following with ideas about the two of them possibly getting married. Sally is undoubtedly a bit baffled by all this at once, and she doesn't jump on this not-so-exciting train of thought. Holden responds by calling her a "pain in the ass," which effectively ends the connection. He is alienated once again by trying to share his innermost thoughts/conflicts.
Holden spends most of his time in physical isolation; part of this seems to be his inability to meaningfully connect with the people around him. He feels alienated from the actions and thoughts of others and even takes measures to alienate himself from the connections he has potential to create. This inner conflict drives the novel, as Holden inches closer to a time when he must leave the world of childhood behind and integrate himself into the more mature world of adulthood.