As the story begins, the nameless male character—a newlywed husband—is taking a really long time to stash his and his wife's luggage in their train compartment. Once he's finally finished, he and his wife—the other main character—make a bunch of exclamations about how they're a married couple now. The wife starts worrying about all the people around the world who get married (and, she seems to imply, have sex) everyday, and whether it works out or not. The husband says not to think about all that stuff.
They discuss the wedding, and (after the wife asks him) the husband says he thought the wife's friend Louise looked really stunning. This seems to irritate the wife, who ends up accusing the husband of ignoring her sister and not liking her family. He strongly objects. After they've (sort of) wrapped this argument up, however, they begin bickering about the wife's hat. She asks the husband if he likes her hat, and he says that, while he's sure it's "probably great", he really likes her old blue hat. The wife is irritated and says that the old hat was cheap.
This leads into another, perhaps even bigger argument, where the wife says the husband hates her hat and should've married Louise, who probably shares his taste in women's hats. The husband says she should've married Joe Brooks—a traveling salesman friend of hers—and she says that maybe she should have. Then, she further attacks the husband for thinking about Louise while standing by the altar, in the presence of God, waiting to get married.
The husband apologizes and says it was just a weird, funny thought he had. The wife worries more about how the marriage will turn out, and they talk about what they'll do once they get to New York for their honeymoon. She says she might write letters to some people from the wedding, annoying the husband. But then they agree to just stay in the hotel room and do "whatever we [want]" to do (clearly meaning consummate the marriage).
They make out or something during a period of silence (Parker leaves it ambiguous), and agree not to fight anymore. Right after that, however, they end up arguing more about the hat. The story ends pretty much where it began with the couple wondering and puzzling over the fact that they're both married to each other.