Young Henry Aldrich would like to "win" a trip to Alaska. But in order to participate, he first has to put up $100. The whole matter sounds awfully fishy. Henry and his pal Dizzy go into the soap business. Their attempt to raise money turns into a disaster when they get the soap formula wrong. But the Alaska trip is really on the level. It's been organized by Sylvanus Q. Sattherwaite, businessman and philanthropist. But Henry still doesn't have the money...

Inspired by an advertisement to join an educational summer trip to Alaska, Centerville teenager Henry Aldrich writes to Sylvanus Q. Sattherwaite. Before Henry is accepted, Sattherwaite, who lives in Chicago, stipulates that Henry must earn $100 for the trip and must get three recommendations from adults. Henry's father Samuel thinks that his son is being duped by mail fraud and insists that Henry drop the idea. Henry nevertheless sends the addresses of civil engineer Bill Van Dusen, laundry woman Cleopatra Johnson, and neighbor Joseph Anderson for Sattherwaite to gather the recommendations. After Henry is publicly disgraced at a movie theater because the manager accuses him of cheating on bank night, his friend Bill inspires him to earn money by making and selling soap bars, which Henry and his friend, Dizzy Stevens, make in a big tub in the Aldrich family basement. Success comes when Henry's friend, Kathleen Anderson, encourages him to have local kids sell the soap on commission to their families. One evening, Henry's parents host a dinner party at their home for representatives of the International Canning Company, which is considering building a mushroom-canning factory in Centerville that will use locally grown mushrooms. Henry leaves a saucepan filled with soap in the kitchen and the Swedish cook, Anna, mistakes it for her mushrooms. The dish is inedible and the nauseated guests are further surprised when Henry's soap factory explodes. The canning representatives leave the next day and the entire town, whose clothes have disintegrated because of Henry's homemade soap, blame Henry for the disaster. When Sattherwaite writes to Anderson asking for a recommendation, Anderson describes Henry as a "scatterbrained, witless, destructive, asinine and reprehensible boy." Sattherwaite's interest in Henry is piqued by this description because he believes that most troublesome boys are just boys with too much undirected energy. Henry's father demands that Sattherwaite refund Henry's earnings and accuses him of fraud. Unknown to Samuel, however, Sattherwaite is the head of the International Canning Company, and when he returns the money he mentions that "canning toadstools is also a federal offense." Bill encourages Henry not to give up, and so Henry hitchhikes to Chicago. Sattherwaite's secretary will not let him in, however, and he only gets in when he is mistaken for the fan mechanic. Henry "fixes" the fan by plugging it in, but the wind blows Sattherwaite's papers out the window and Henry leaves in disgrace. Sattherwaite is impressed by Henry's perseverance after he learns of his true identity and goes to Centerville. Sattherwaite receives a cold reception in town, and matters get worse when Bill knocks him out because he thinks that Sattherwaite hurt Henry in Chicago. Sattherwaite is thoroughly disgusted and prepares to leave when Henry visits him at his hotel. At first, Sattherwaite is put off because nosy reporters try to push him around for a story, but he finally sits quietly with Henry who explains that despite his best intentions, he always seems to be in the wrong place at the wrong time. While they eat dinner, Sattherwaite encourages Henry and is delighted when he tastes the local mushrooms and finds them to be delicious. Henry accompanies Sattherwaite out of the hotel, and astonished town leaders learn that Henry is responsible for Sattherwaite's reconsideration of their town for his factory. Sattherwaite promises to take Henry to Alaska.