The movie opens with a bakery truck driving down the street, and Beaver and Wally riding together on Wally’s bicycle, delivering morning newspapers. Beaver tosses the newspapers wildly into the air with both hands: one of them plops into a wet cement, another one lands on a roof, one into a dog’s mouth, one into a birdbath, one onto a cat, one into a man’s leaf-vacuum nozzle, and one lands smack on a painter’s head. Then the leaf vacuum explodes and throws dirt through the truck driver’s window, causing him to slam on his brakes and have his sticky pies thrown about. Beaver and Wally apologize then ride away.
Beaver has his heart set on a bicycle in a store window, but does not think his parents will buy it for him. Eddie Haskell tells him that if he flatters his father by signing up for football, he will get it on his birthday. Beaver joins the football team and endures the practices, despite his disadvantage of being smaller than his teammates. Beaver even goes so far as to refuse his father reading him a bedtime story and kissing him goodnight. Beaver looks forward to his first football game. Ward is glad Beaver signed up for football, but the first game ends poorly when Beaver is tricked into passing the ball to a kid on the opposing team, whom Beaver remembered as a friend from summer camp. When Beaver celebrates his birthday, where guests eat cake and play spin the bottle, he is presented with the new bicycle, as well as a computer.
On the first day of school, five days later, Ward and June tell Wally to accompany Beaver for a few days while Beaver gets used to riding his bicycle to school. Beaver has a kind new teacher named Miss Landers. After school, Eddie asks Wally to come to the soda shop to see him flirt with Karen. Eddie does not want the Beaver to follow them, so Wally leaves him alone at the bike rack, telling him he will be back for him. Beaver is polishing his bike when a teenaged boy comes over and asks if he can show Beaver some cool bike tricks. Beaver agrees and the boy shows him some tricks before riding off with the bike. Inside the soda shop, Karen likes Wally and not Eddie. When Wally and Eddie come out of the shop and hear that Beaver’s bike was stolen, they look for it, but cannot find it. During dinner that night, the boys try to cover up for the missing bike. When Ward finds out the truth, he is upset with the Beaver, but angrier at Wally because he was responsible for watching Beaver. In the boys’ bedroom, they get into a fight, which sends Beaver’s new computer flying out the window. Wally grabs the wire and tries to pull it in, but the wire breaks, and it crashes into pieces. This results in Ward completely losing all of his patience and grounding the boys.
After the grounding, Beaver skips football practice and studies; and Wally spends time with Karen, who breaks up with him after reuniting with her ex-boyfriend, Kyle. Beaver goes into the city and gets hit by a truck, but is unharmed. Beaver encounters the guy who stole his bike. The youth, who is the younger brother of Kyle, challenges Beaver, as a way of getting his bike back, to climb up to a gigantic coffee mug atop the local cafe, which Beaver falls into and can’t get out. The fire department and Ward help get him down, Ward realizing the Beaver may be under too much pressure. Ward had found out about Beaver skipping football practice and says Beaver can quit the team; but Beaver rejoins the team. During the last game, he catches the ball and scores a touchdown, while chasing after his stolen bike. At the Mayfield Festival, he again encounters the boy on the stolen bike and chases him. Kyle trips the Beaver to help his little brother escape, and Wally retaliates by pushing Kyle into a tub of fudge. Karen is also put off by Kyle’s bullying and leaves him for Wally. Beaver uses a concession stand to block the boy’s way, causing the boy to fly across a judges’ table of pies set up to be judged and into an entire cart of them. Beaver gets his bike back. At home, Ward sees him polishing it; tells him that it would be safer if it stays in the house; and, at Beaver’s request, reads him a bedtime story.