The novel is a first-person account narrated by Kenneth Watson, who lives in Flint, Michigan with his parents, Daniel and Wilona Watson, his older brother Byron, and younger sister Joetta. The opening chapters establish Kenny as a very bright and shy 4th grader who has difficulty making true friends until Rufus Fry arrives in town from Arkansas. Rufus is also bullied by the students at Clark Elementary for his "country" clothes and accent, making Kenny reluctant to befriend him at first, but they are soon inseparable. Kenny is alternatively bullied and protected by his 13 year old brother Byron, whom he calls "an official teenage juvenile delinquent". Byron has been retained twice because he often skips school and is still in 6th grade. He invents a series of "fantastic adventures" which constantly get him into trouble and include playing with matches in the house and setting things on fire, abusing his parent's credit at the corner grocery store to buy himself treats, and getting a "conk" hairstyle against his parents' orders.
Daniel and Wilona eventually become so frustrated with their inability to "straighten out" Byron that they decide to send him to Birmingham, Alabama to live with Grandma Gloria Sands (Wilona's mother) for at least the summer and possibly an entire year. As soon as the school year concludes, the Watsons ready their car ("the Brown Bomber") and embark on a road trip from Flint to Birmingham to deliver Byron to his grandma. Kenny had been looking forward to the "battle royal" between his grandma and Byron, but is disappointed when just a few sharp words from the "old, old lady" have Byron speaking respectfully and generally behaving himself, causing Kenny to seek out his own "adventures". Grandma Sands warns the children to avoid a particular local swimming hole because of a dangerous whirlpool, which Kenny misheard as "Wool Pooh" due to her thick Alabama accent. Kenny wants to swim there anyway, and is frustrated when Byron and Joetta refuse to go along. Ignoring the warnings of both Grandma Sands and Byron, Kenny jumps into the seemingly tranquil pool and edges deeper and deeper water until the whirlpool catches him and almost pulls him down, but Byron saves him. Remembering his grandmother's words, he imagines that a strange monster he thinks is the mysterious Wool Pooh swam up from below to grab his ankle and pull him under. Byron later insists that there was nothing else in the water, but Kenny is convinced that the Wool Pooh actually exists.
Shortly afterwards, a bomb goes off at a nearby church where Joetta is attending Sunday school. Kenny wanders into the still-smoking church in the immediate aftermath looking for his sister, but instead sees the Wool Pooh in the smoke clinging to a torn girl's shoe that looks like Joetta's. In shock, he walks back to Grandma Sands' house without anyone noticing that he had been at the church, and he's again shocked and confused to find Joetta already there. She claims that it was Kenny who had called her away from the church and led her home, and she does not even know that a bombing had taken place right after she'd left Sunday school.
As soon as they realize that Joetta is safe, the Watsons decide to immediately return home to Flint, trying to avoid explaining the full implications of what has happened to the children. Kenny is unable to process the events in Birmingham and avoids his family and friends over the ensuing weeks, instead spending many hours hiding behind the sofa. Byron eventually coaxes him out and gets Kenny to talk about what happened, which finally brings a flood of tears from Kenny. Encouraging his little brother to "keep on stepping", Byron explains that although the world is not perfect, he has to keep moving on.
