The film is set in Coalwood, West Virginia in the year 1957. The coal mine is the town's largest employer and almost every man living in the town works in the mines. John Hickam (Chris Cooper), the mine superintendent, loves his job and hopes that his boys, Jim (Scott Miles) and Homer (Jake Gyllenhaal), will one day join him in his mine. When it appears that Jim will receive a football scholarship to attend college, this leaves Homer to fulfill his father's dream, although his mother, Elsie (Natalie Canerday), hopes for more for her son.
In October, news of the Soviet Union's rocket launch of Sputnik 1 reaches Coalwood. As the townspeople gather outside the night of the broadcast, they see the satellite orbit across the sky. Filled with awe and a belief that this may be his chance out of Coalwood, Homer sets out to build rockets of his own and enter the science fair. Initially, his family and later his classmates think he has gone crazy and is wasting his time, especially when he teams up with Quentin Wilson (Chris Owen), the school's math geek who also has an interest in rocket engineering. With the help of his friends, Roy Lee Cooke (William Lee Scott) and Sherman O'Dell (Chad Lindberg), and support from their science teacher, Miss Riley (Laura Dern), the four try out their new passion. While their first launches are failures, they begin experimenting with new fuels and rocket designs. After several successful launches, the local paper runs a story about them.
The next day, they are arrested accused of having started a forest fire with a rocket that had gone astray. After John picks up Homer from the police station, Roy Lee is seen getting beat up by his stepfather, Vernon. John intervenes and rescues Roy Lee, warning the drunken man that, even though Roy Lee's father is dead, he will fight for Roy Lee as Roy Lee's father would have. In a rare display of emotion, he tells Roy Lee that Roy's father was one of the best men who ever worked for him.
The arrests, along with John's lack of support, crushes the boys' dream and they abandon rocketry.
After a mine disaster, John is injured while rescuing "... a dozen men [who] would have died...", though one other miner does die (Ike Bykovski). Homer drops out of high school and works the mine to provide for the family while his dad recovers.
Later, Homer is inspired to look at a rocket science book Miss Riley gave him, and learns how to calculate the trajectory of a rocket. This reveals that an unrecovered rocket launched by the boys could not have caused the fire, as it was unable to travel that far. Homer and Quentin calculate the precise distance of the missing rocket and find it in a stream. The boys present their findings to Miss Riley and the school principal, Mr. Turner (Chris Ellis). Chagrined at the police, Turner identifies the offending projectile as a flare from a nearby airfield.
Homer returns to school, the boys return to rocket making, and soon win a school science fair. The school decides to send Homer to the national science fair in Indianapolis, Indiana. That night, John is almost shot by a man in a black car outside. John, with Homer and Jim in tow, exits the house to see who fired. John shouts "Vernon!" realizing this was apparently revenge for the threats John gave Roy Lee's stepfather earlier. Homer and Jim express their concern about this to their father, but John passes it over, bitterly telling Homer to go "look for his suitcase" (Homer had been doing so prior to the shooting). Fed up, Homer confronts his father and a heated argument ensues. Homer storms out of the house, vowing to never return or look back.
At the national science fair, Homer's display is received very well. Overnight, someone steals his de Laval nozzle, as well as his autographed picture of Wernher von Braun. Homer makes an urgent phone call home for help. Elsie implores John to end the ongoing strike so that Mr. Bolden can use the mine's machine shop to build a replacement nozzle. John initially refuses but relents when Elsie, fed up with his lack of support for their son, threatens that she will have to leave him. With the support of the town, Homer wins the top prize and is besieged with scholarship offers from colleges. He is also congratulated by his inspiration Dr. von Braun, but in the confusion does not realize the engineer's identity until after he is gone.
Homer returns to Coalwood as a hero, and visits Miss Riley, who is now ill with Hodgkin's disease. He shows her the medal he has won, and she responds touchingly. A launch of their largest rocket yet (called the Miss Riley) is the last scene of the film. (In the reality of which this scene is emblematic, the rocket boys' most successful rocket reached an impressive altitude of 30,000 feet (9,100 m) higher than the summit of Mount Everest.) John finally shows up for a launch, and is given the honor of pushing the firing button. As the rocket streams upward, the film shows the view from the perspectives of many characters. As the group looks up to the rocket, John slowly puts his hand on Homer's shoulder and smiles.
A series of vignettes (including footage of a Space Shuttle launch and home movie footage of the characters in the 1950s) reveal the outcome of the main characters' lives.