To come of age means to move as a teen or child from a place of innocence into experience. The question you must ask is, In what ways is Connie innocent, and how is that innocence changed into experiential knowledge (if not destroyed)?
At first glance, Connie seems fairly astute for a fifteen year-old when it comes to the opposite sex, perhaps too "sharp," for her age, in that she's very interested in boys and knows how to manipulate them to get their attention. She knows how to handle her mother in that she reveals only what she needs to, engages in the social activities she wishes to without her mother knowing, and seems to have the world under her control. Note how at the diner she gains the boy she wants and disappears with him down a dark road to engage in vague activities (but clearly, whatever happens, the encounter is characterized and romantic and pleasant enough for her. She is not traumatized). We don't get clear information that she is sexually active, but several hints, so in this way, Connie is not ignorant of what goes on between boys and girls, nor has she paid the price for an unhappy relationship through heartbreak or pregnancy, far as we know.
But she is extremely unwise about how she deals with Arnold Friend and Ellie when they show up in her driveway when her family is gone.
Examine that scene and identify all the ways that Connie makes the mistakes of an ingenue. Where would you advise her to not make a certain statement or take a certain action? How does she fall prey to the verbal manipulation by Arnold Friend? How would an adult handle someone such as Arnold Friend?
Two areas to examine where Connie comes of age are "relationships" (how one deals with people such as strangers and/or the opposite sex) and "self-image," especially as it relates to vanity. If Connie had more negative experience with relationships, would she have taken this chance talking to Arnold? If Connie had ever been less than attractive or bottom of the social totem pole, might she not have been quite so vain in this circumstance, or overconfident to think she can survive anything? Note the eNotes themes summary for some additional analysis and tips. The eNotes criticism also shares several critics' views about Arnold Friend ("an old friend"?) as the devil who's here to teach us all a lesson about ourselves.
The ending of the story is very disturbing, as we know that there is no escape for Connie. It is a horrific consequence, a terrible price for her ignorance -- rape and, we assume, even death. Connie doesn't have the opportunity to learn from her wisdom and move into adulthood.
Again, look for quotes that show her innocence and inexperience, where she is tripped up by her lack of knowledge. The final moments of the story show her awareness of how trapped she is, how the end is near. (Especially note when she has sunk to the floor and has the phone in hand.) And in the final image, how do we know "this is it" for Connie? What resonance does the light and the quality of Arnold's voice reveal about where Connie is going?
Also examine the title: how does it speak to coming of age?