We get to meet Holly in this short but rather telling chapter. The narrator first notices her mailbox after living in the apartment for a week, and it's the mailbox name-card that draws his attention. The printed card reads "'Miss Holiday Golightly'; and underneath, in the corner, Traveling" (2.1). Something about this sticks with the narrator, "like a tune" (2.1).
The narrator then recalls the night he first actually sees Holly. It's after midnight and Mr. Yunioshi wakes him up when he yells down to Holly, "Miss Golightly! I must protest!" (2.2). It seems that Holly has lost her keys to the front door of the apartment and has rung Yunioshi's bell to get him to let her in. She apparently does this all the time and the photographer angrily reminds her that he needs his sleep since he has a job. She implores him not to be angry and teases him by telling him that she "might let [him] take those pictures [they] mentioned" (2.7). (Pretty racy!) When he asks her when they can take the pictures, she just tells him, "Sometime" (2.10).
The narrator tries to catch a glimpse of Holly without her seeing him, and he gives us a pretty detailed description of her. She has "ragbag colors [in] her boy's hair, tawny streaks, strands of albino-blond and yellow" (2.21) and she's dressed in "a slim cool black dress, black sandals, a pearl choker" (2.12) (This is the look that Audrey Hepburn made famous in the film version.) She's quite thin, and "[has] an almost breakfast-cereal air of health, a soap and lemon cleanness, a rough pink darkening in the cheeks. Her mouth [is] large, her nose upturned." And "a pair of dark glasses blot[s] out her eyes" (2.12), even though it's the middle of the night. The narrator finds it hard to figure out Holly's age since she looks older than a child but younger than a grown woman (it turns out that she's almost nineteen at this point).
Holly has a man with her who is "short and vast" (2.13), and when they get to her apartment the narrator sees this man kiss Holly's neck (she doesn't seem to notice the man, however). Holly thanks him for walking her home and starts to close the door to her apartment. The man protests, and when Holly calls him by the wrong name (his name is Sid Arbuck and she calls him Harry), it's pretty clear that Sid expects something in return for paying for dinner for Holly and her friends: "Didn't I pick up the check, five people, your friends, I never seen them before? Don't that give me the right you should like me? You like me, baby" (2.18). Clearly, he's interested in more than just "liking" Holly.
Holly won't open the door, and Sid gets ready to kick it in (real charmer, isn't he?) but instead falls down the stairs. Holly hears the commotion and opens the door to her apartment, which Sid thinks is a sign that she's changed her mind and wants to "like" him after all. But she quickly put him in his place when she tells him, "Oh, Mr. Arbuck. […] The next time a girl wants a little powder-room change […] take my advice, darling: don't give her twenty-cents!" (2.22). We're not exactly sure what to make of this comment, but it seems like Holly is accusing Sid of being cheap.