Haruki Murakami is a surrealist, so this plot is bizarre and sometimes almost random.
Part One: "The Thieving Magpie"
Toru Okada tells the reader of his attempt to find the missing house cat for his wife. Kumiko, the wife, tells him to check the alley behind the house, so he does, but instead of the cat, Toru finds a mysterious, flirty teenager named Kasahara. The implication is that she is some sort of vagrant orphan, or perhaps a mysterious visitor. They enjoy a drink behind an abandoned house. He falls asleep in a pool chair, wakes up to find the girl missing, and continues back to his house. At the house, he receives calls from a strange woman who seems to be masturbating on the other side of the line. Also, Malta Kano calls and requests a meeting with Toru.
Kumiko calls again to recommend that Toru meet with Malta Kano, a clairvoyant psychic, claiming that she can help the couple find their missing cat. Malta Kano is a friend of Kumiko's brother, Noboru, which actually happens to be the cat's name too, in a weird coincidence. This isn't the first time she has urged him to see a witchdoctor of some sort—there was Mr. Honda before, a strange old man whose "psychic" powers were just him endlessly reciting his war stories.
At a local hotel, Toru meets Malta Kano and her sister Creta. Creta reconvenes with Toru at his home later and tells the story of Creta's unfortunate violation—she was raped by Kumiko's brother Noboro. She leaves. Kumiko comes home wearing a new perfume, and he suspects it was a gift from an unknown man. When Lieutenant Mamiya calls to tell him Honda has died, Toru learns that Mr. Honda left something to him in the will. Mamiya swings by to give Toru his small inheritence, and he tells a strange story about war in Manchukuo where he witnessed a man skinned alive by the Kwantung Army. When he leaves, Toru checks the box with Honda's gift and discovers that it's empty. The gift is nothing.
Part Two: "Bird as Prophet"
Now Kumiko herself has gone missing. Toru learns from Noboro and Malta that Kumiko has indeed been sleeping with a new man, and she really likes him, so she's leaving Toru now, probably forever. Toru is distraught. To distract himself, Toru goes to May Kasahara, and they go to the bottom of a well, and then into the city to people watch. May's work is counting the bald heads of men for a wig company. The antics fail, and Toru cannot help but remember his wife, their first date where they watched jellyfish. In a surrealist image, Toru imagines a hotel room with a woman. He notices a blue line on his face. Toru meets a woman with a singer, and he knows the singer from his personal past. Toru follows them, and the singer turns violent. Toru gets away by defending himself with a bat.
Part Three: "The Birdcatcher"
The woman Toru met is actually Nutmeg. He returns to another day of people-watching, and sees her again. They discuss some work, and she hires him to pleasure middle aged and elderly women who pay for him. He thinks about the dread and humiliation of prostitution. The blue mark never went away. Toru's new income helps him to buy the abandoned house. Nutmeg has a son named Cinnamon who takes care of the house and fixes the well. Toru still goes to the bottom of the well.
Then one day, Toru sees the missing cat. Toru arranges an internet chat to talk to his separated wife.
Suddenly it clicks: Toru discovers that he has been enchanted by a witch, and he leaves the bottom of the well and finds the hotel room and he confronts Nutmeg, who is actually Kumiko all along. He learns that Noboru was badly beaten into a coma by a man with a baseball bat. Toru fits the description. Then a man enters the hotel room and attacks Toru with a knife. Toru (perhaps unsurprisingly) kills that man with, you guessed it, a baseball bat.
Back at home in his lonely well, Toru is succumbing to the rising waters, but Cinnamon saves him. Nutmeg finally clarifies a few days later: Yes, Toru is under a supernatural curse, and in reality, Noboru just had a stroke, and that's why he's really in a coma. Kumiko decides to pull the plug keeping Noboru alive, killing him. May tells Toru that Kumiko succeeded, and Toru says he will wait for her, even if she has to serve a sentence in prison for her crime.