Attention: spoilers all over the place below. Read the story first. Seriously.
The Very Short Story
Boy meets girl, girl plays hard-to-get, girl dies, boy goes back to older lover in Geneva.
The Slightly Less Short Story
Frederick Winterbourne is bored by his life. He mostly hangs out with older ladies: visiting his elderly aunt in her European homes and engaging in some kind of affair with an older woman in Geneva.
In Vevay, Switzerland, he meets the vivacious young Daisy Miller, a girl from Schenectady, NY traveling through Europe with her clueless mother and badly behaved little brother, and his world is turned upside down. He likes Daisy, but her erratic, flirtatious behavior confuses and irritates him.
The following winter, he meets up with Daisy in Rome only to find she's been flirting like crazy with all of the Italian dudes. (Come on, who wouldn't?) She starts hanging out a little too intimately and a little too publicly with an Italian social climber named Mr. Giovanelli. People start to talk, and Winterbourne is torn: is Daisy tacky and ridiculous or hot and fun? And is she engaged to Giovanelli or not? He can't get a straight answer.
Winterbourne tries to get Daisy to tone it down and she makes fun of him for being boring. He almost loses it when he sees her out alone at night with Giovanelli at the Colosseum, a location where people typically contract Roman fever (malaria).
A few weeks later, she's sick as a dog. Yep, she's got malaria. When she dies, her mother passes on a message to Winterbourne: Daisy wanted him to know she was never engaged to Giovanelli.
After thinking this through, he decides he should have made a move when he had a chance instead of nagging her like a nerdy older brother. At the end, he concludes he's "lived too long in foreign parts" (2.276). Poor thing.