According to Violet, Finch is "a Bartlett legend" (2.47). "Everyone knows of him," she tells us. (Can you hear the awe in her voice?)
Some people hate him because he's weird and he gets into fights and gets kicked out of school and does what he wants. Some people worship him because he's weird and gets into fights and gets kicked of school and does what he wants. (2.47)
Guess which group of people Violet falls into?
Finch may come across as a lot of things—a rebel and a rocker among them—but what we see as readers is a scared high school senior with a lot on his plate. It's not that he's worried about girls, or graduation, or college, like some of the other kids his age. Finch has bigger fish to fry: a super dysfunctional family (including a violent father), some terrible bullying at school, and a raging case of bipolar disorder that is actively trying to kill him.
He ain't your average high school boy.
The most important thing to know about Finch is that even though he thinks about suicide all the time—we're talking breakfast, lunch, and dinner—he doesn't want to die. Through most of the book, we see him wage a war against his bipolar disorder. He tells us:
I want to stay alive. I'm fighting to be here in this shitty, messed-up world. (1.92)
He also tells us, heartbreakingly,
I'm most afraid of me. (32.13)
Finch is afraid of a lot of things, actually, including treatment, because he considers mental illness a label that stays with you for life. Instead, he deals with his symptoms alone. He refers to them privately as the "Awake" and the "Asleep" (which are his manic and depressive episodes, respectively).
When we meet Finch on the ledge of a sixth-story window, he had only recently woken up from a long period of the Asleep—and he'd do anything to keep it from happening again.
Finch deals with his bipolar disorder as best he can. He runs almost every day, sometimes going as far as neighboring towns. He thwarts his own suicide attempts at least three times that we see. He even drags himself to a suicide support group.
Despite his best efforts, though, Finch sometimes "hulks out." For someone who doesn't come across as a violent most of the time, he has some alarming tendencies. (Whether this stems from his father's abuse, his bipolar disorder, or both is hard to say.)
When he's bullied by Roamer, Finch says he feels
[…] a familiar black grenade of anger—like an old friend—go off in [his] stomach, the thick, toxic smoke from it rising up and spreading through [his] chest. (3.28)
That sounds awful, doesn't it? Well, it's also awful when he tries to drown and choke Roamer to death on two separate occasions.
There's a lot of gloom surrounding Finch, which is probably inevitable for a character who commits suicide. That said, he'll be remembered by Violet (and us, of course) for his good qualities.
Finch himself had a hard time seeing those good qualities, though. In his worst moments, he felt broken and undeserving of love. Also, he often felt uncomfortable in his own skin, trying on different looks and personas (love you, '80s Finch) like he's in the dressing room at J Crew. Before he died, he asked himself:
Which of the mes is me? There is only one me I've ever really liked, and he was good and awake as long as he could be. (49.2)
The "me" he liked was the one we saw through most of the book—the guy who was funny enough to charm a girl when she's on a narrow window ledge. The guy who saw real beauty all around him when other people saw plain ol' Indiana.
Despite his own problems, or maybe because of them, Finch was a gifted counselor, encouraging Violet to "get back on the camel" (as Mr. Black would say) after her sister's death (3.30). He was a talented musician and an endless source of creativity who inspired the people around him. He was selfless—the kind of guy who makes you dinner on his own birthday.
And he was also hopeful, even though the world didn't give him much reason to be.