Margo Roth Spiegelman is the girl who "loved mysteries so much that she became one " (Prologue.35), and while in school, she seems intent to be the manic pixie dream girliest of them all.
She runs away from home occasionally to allegedly learn to play guitar in Mississippi, or spend three days traveling with the circus because "they thought she had potential on the trapeze" (1.1.21). (This is highly unlikely because actual circus performers are trained professionals, not just runaways who are "all curves and soft edges" (1.4.86).) She snuck her way backstage at a concert, had some underage drinks, and then "rejected the bassist" (1.1.21), making her both edgy and virginal, every antisocial nerd's dream. Margo Roth Spiegelman is basically the "cool girl" that Amy Dunne hates so much.
Margo is often cool and aloof. "She never acted as if she liked anyone all that much" (1.1.35), and she refers to her "friends" as her "various and sundry minions" (1.2.41). Not a social circle we'd want to be in. She's also self-absorbed, illustrated by the fact that "she never really asked [Quentin] any questions" (1.3.1); she only talks about herself.
She's "the most horribly self-centered person in the history of the world" (3.22.59) (her words, not ours) and destructive. When she learns her boyfriend is cheating on her, she vandalizes his car and property, along with that of pretty much everyone connected to him, which is going to hurt these kids' parents (who have to pay for this stuff) more than the kids themselves. But Margo Roth Spiegelman, despite her obsessive, planning nature, is unable to see past her own anger.
We're not sure why Quentin likes Margo Roth Spiegelman since she drags him around and kind of treats him like poop. She's way more fun than he is, though, which probably explains why he latches onto her—he's getting good grades, and she's mischief.
The she disappears, cementing her status as a teenage gone girl. We can understand why she'd leave: No one at school really understands her (her fault) and her parents aren't the warmest or most welcoming people in Florida (not her fault).
Quentin thinks Margo Roth Spiegelman is leaving clues so he can find her, but that's because he's still picturing her as some sort of super-human goddess instead of what she really is: a teenage girl. Quentin realizes during his quest to find her that Margo is "Someone who—because no one thought she was a person—had no one to really talk to" (2.15.21). Bummer.
It turns out she doesn't want to be found, but it's a good thing Quentin does, because they're able to finally define themselves instead of letting others define them. Margo speaks to how important this is, saying, "I can't be you. You can't be me. You can imagine another well—but never quite perfectly, you know?" (3.22.155). Truth, yo.
The problem is that Margo Roth Spiegelman has been doing this to a fault: manipulating people into thinking she's more amazing than she really is. She blames others for thinking she's superhuman, but she's the one who started it—she even admits it, saying, "People love the idea of a paper girl. They always have. And the worst thing is that I loved it, too. I cultivated it, you know?" (3.22.96). If no one knows Margo, then, this is ultimately her creation.
So what's Margo Roth Spiegelman going to do about it? It seems that she's doing a lot of introspection instead of trying to be a perpetual extrovert. She has started reading a lot, and even quotes Emily Dickinson. Quentin tries to get her to return home to Florida with him, but she refuses. She's at least learned one thing about herself while she's been gone: She has to find a home where she belongs, and where she can be herself.