Our protagonist - and the voice-over we hear at a number of points throughout the movie - is Greg Gaines (Thomas Mann), who hates both high school and himself and avoids social contact as much as possible. He hangs out with Earl (R.J. Cyler) a lot - Earl is his "co-worker" in that they make deliberately horrible movies together, and have done so since they were about 10. When Greg's mother finds out that his schoolmate and former childhood friend Rachel (Olivia Cooke) has leukemia, she forces him to spend time with Rachel. Despite a very rocky start, they turn out to have a fair bit in common and spend a lot of time together.
I've been putting off reviewing the movie for a couple days as it keeps shifting in my memory as I tried to make it out. It's a bit unconventional, but who really wants conventional? There are way too many of those in the world. And the more I think about this, the more I think it's well served by its lack of normalcy. What I was most bothered by was that all the adult characters (in fact all characters except the three in the title) are caricatures. The parents in particular are worse than useless. But I think the biggest piece of the puzzle that fell into place for me was the realization that this is Greg's movie: we see what he sees, and that's how adults look to an alienated teen.
We have a tendency to like and trust our narrators and protagonists, although we have no particular reason to do so. So you realize only slowly (because we're hearing his logic about his behaviour, which is internally consistent) that our narrator is pretty messed up. About half way through the movie it's all laid out very clearly by Earl for Rachel (Earl is a character too, but he knows Greg well). Then you focus on Greg's flaws for a while and like him less. But in the end, you see him through her eyes - and see not only the flaws, but the potential. The movie yanks you about, but in the best possible way and - oddly - without feeling manipulative. I liked it when I watched it, but it's grown in my mind over the last couple days from "good" to "great:" memorable and exceptionally well done, a very rewarding character study.