At Ralph Waldo Emerson High School, bookish student Barney Springboro (Scott Baio) performs various scientific experiments on laboratory mice until his friend, yearbook photographer Peyton Nichols (Willie Aames), retrieves him for a class assembly. Peyton questions Barney's disinterest in finding a girl friend as the students rally in preparation for an upcoming baseball game against a rival high school. Afterward, Peyton seduces one of the school administrators, Corinne Updike, and Barney returns to his experiments.
At the insistence of the pesky class president, Bernadette (Felice Schachter), Peyton promises to take photographs of Barney posing with the genetically modified orchids he has been growing for the school principal, Walter Coolidge. Barney drops the beaker containing the mice's feeding solution, producing a cloud of shimmery smoke that knocks him unconscious. Sometime later, he awakens and returns home, where his uptight mother chastises him for his tardiness and antisocial behavior. As she yells, Barney's bedroom door mysteriously slams shut. During English class the next day, Barney fantasizes about a popular girl named Jane Mitchell (Heather Thomas). When the teacher, Rose Burnhart, calls on him unexpectedly, Barney furrows his brow, causing the map above the chalkboard to fall on her head.
That afternoon, Peyton asks Jane on a date, but she reminds him that she has a college-aged boyfriend. As Barney stares at Jane's chest, her cardigan bursts open, leaving everyone confused. In the lab, Barney experiments with his new telekinetic abilities by levitating various objects across the room, unaware of Bernadette and Peyton are watching through the window. When his friends confront him, however, Barney convinces them to keep his powers a secret. At home, Barney propels his model spaceship through the air, imagining the crew members inside have come alive. He then animates a ventriloquist dummy, which frightens Mrs. Springboro so much that she believes her son is possessed.
On the day of the big baseball game, Barney manipulates the ball and hits the winning home run. Meanwhile, Principal Coolidge attempts to break into Barney's lab to check the growth of his orchids, but cannot obtain the key. After Barney agrees to let Bernadette write a report about him for her older sister's college science journal, they notice Mrs. Burnhart sneak into his lab and uncover a pot of Peyton's marijuana hidden behind the orchids. She retrieves Principal Coolidge, but they return to discover the plants are missing. Baseball coach Dexter Jones finds Barney and Bernadette stuffing the plants in the incinerator, and the smoke causes him to become intoxicated: under the influence, he imagines riding a bicycle with Albert Einstein while being chased by his wife, who is dressed like a Viking warrior.
Over the weekend, Barney, Peyton, and Bernadette go to a pre-graduation celebration at an amusement park, during which Peyton challenges Jane's boyfriend, Robert Wolcott, to a beer-drinking contest. While on a spinning ride, Barney increases the speed of Robert's compartment, causing him to vomit and lose the bet. That night, Peyton brings Jane home and seduces her by pretending to act older and more mature. Meanwhile, Barney and Bernadette have dinner and talk about former crushes. The pair spend the next afternoon together in the park before returning to Barney's lab, where they make love.
At school on Monday, Jane admits that she regrets having sex with Peyton and returns to her boyfriend. Robert, however, invites Peyton to a casino-themed college fraternity party with the hopes of winning the money owes him for the drinking contest. Peyton begs Barney to attend so he can manipulate the roulette wheel, but Bernadette becomes angry that he would use his powers to gamble. Meanwhile, Mrs. Updike convinces Principal Coolidge to respond to a personal advertisement in the newspaper to meet a woman for a date.
At the restaurant, Principal Coolidge discovers that his date is Rose Burnhart, and the two finally succumb to their long-time attraction by having sex under the table. During the fraternity party, Barney attempts to manipulate the roulette ball, but causes a commotion among the guests when he accidentally levitates the entire wheel. When Bernadette refuses to answer his telephone calls, he spends the night in his laboratory drinking whiskey. Hung over the next morning, he apologizes to Bernadette and arranges to meet her at the prom that evening. Before he leaves for the dance, however, Mrs. Springboro hires two priests to perform an exorcism on her son, and Barney uses his ventriloquist dummy to chase them around the house so he can get away.
Peyton and Jane are crowned prom king and queen, and Jane rejects Peyton's continued advances. As Barney dances with Bernadette, Peyton ruins the moment by offering his friend airplane tickets to Las Vegas, Nevada, where they can continue gambling. When Robert confronts Peyton about the roulette game, Peyton apologizes and gives him a packet of nude photographs he took of Jane. Enraged, Robert attacks, and Barney uses telekinesis to summon a large gust of wind that tears off the students' clothes and sends everybody running outside. A wayward fire hose knocks Barney unconscious and he wakes up believing that he has lost his powers. However, while leaving the school, Barney grabs Bernadette by the waist and propels them through the night sky in a cloud of shimmery dust.