Maintenance man Cleveland Heep (Paul Giamatti) tries to keep up with the needs of his many tenants. He comes to realize someone is swimming in the pool after 7 p.m., which is not allowed. The pool cleaner also brings to his attention that there seem to be globs of some sort of hair in the pools filter that have accumulated in just one day. One night, when he is very tired, he hears splashing in the pool and thinks that at last he will catch the mystery swimmer. But when he goes to the pool, there is no one there, not even footprints. As he walks around the pool, he hears someone splashing in the water at that very moment. He thinks all he has to do is wait, and they will surface soon enough. He picks up a brush and walks around the pool, takes a bad step, falls, hits his head and rolls into the pool.
In the next scene we find Heep laying on his own couch, and a nude young woman is sitting across from him. There is water on the floor. He asks if she brought him here, but she only nods that she did. He gives her a shirt to wear. She clings to him, saying that she is too scared to go outside. So there he sits, with a young woman in his lap clinging to him who then falls asleep. He is clearly uncomfortable and tries to wake her. He decides he should take her outside for some fresh air, and then he will walk her home. Once outside, however, he is confronted with a growling creature which sends them both screaming back into his house.
Heep needs to know who she is and what the creature is. We learn that her name is Story and that there is a creature hunting her. She is somehow prohibited from telling him who she is or what is happening, but she does tell him that she is a Narf. Heep begins asking his tenants if they have ever heard of a character called a Narf. Upon asking a young Asian student named Young-Soon Choi (Cindy Cheung), she says she has heard of a Narf as part of a bedtime story that was told long ago to her mother, but she doesn't remember much about the story.
Heep continues doing his repairs, and we are introduced to many of the tenants. Between tasks, Heep tries to catch Young-Soon when she is with her grandmother, so he can ask more questions about the story. Though she has no idea why he is asking all these questions, she is happy to do what she can for this oddly curious man. Her grandmother, however, is suspicious as to why a grown man is so interested in a bedtime story.
Frustrated at only getting bits and pieces of the story here and there, he arranges to be invited into the apartment of Young-Soon and her grandmother. Young-Soon tells him to try and act more like a curious child than a man, and it will help to bring out the grandmother's softer side so she will tell him more about the story of Story. After wiggling, eating cookies and dribbling milk down his face, the grandmother is amused and tells him the story.
Meanwhile, Story is walking through his apartment, marveling at various objects. She notices a different-looking book and takes it down and reads it. The book is actually a journal, one that Heep wrote following the tragic loss of his family. When Heep discovers her reading the book, he asks her not to tell anyone of his past; no one there knows the story or that he used to be a doctor. He also needs to check with Story that what he has learned so far is accurate. Though Story cannot actually say, she makes a sign when he makes a correct statement.
It seems Story is a Narf, here to motivate a great writer to complete his work that will have a tremendous positive effect on the future, at which point a giant eagle will come and take her home. But there is a creature called a Scrunt who will try to kill her before she can complete her task. There are many people who live in the apartment comple, besides the writer, who will unknowingly play different parts in helping Story. Heep believes himself to be her "guardian", the one who can protect her from the Scrunt. In a scene that starts out suspenseful but becomes rather light, Heep tries to face down and battle the Scrunt, being coached by Story via walkie talkie, but it soon becomes apparent that he is not the guardian when the Scrunt attacks him. The attack is interrupted by an arrogant movie critic just in the nick of time.
But now Heep has an idea of what he needs to help Story get home. He must cast the roles needed to complete the task from the diverse people that live in the apartment complex. It is such a complex undertaking that he decides to consult the latest addition to the complex, the arrogant movie critic, to help him root out some of the characters described to him. Heep finally concocts a plan, but it is misguided. When it fails, the Scrunt seizes hold of Story and tries to drag her away, but Heep manages to grab hold of her. It is now apparent they have the wrong people for the roles, and they need to rethink them fast.
The pivotal character to find is the "symbolist", who can "read" the situation, giving a much better description of the characters needed and what they all must do. At last, most of the correct people are found, all but the guardian. They all encircle her hoping to protect her long enough for the eagle to arrive. But the Scrunt is patient and wily and finds a way to get close to her unseen.
Finally, the guardian appears and stares the Scrunt down. We hear the eagle and Heep says goodbye to Story. He realizes she has saved him from hiding himself away, and then she is gone.