On the night of July 4, 1978, in Fort Lauderdale, Florida, 12-year-old David Freeman walks through the woods to pick up his 8-year-old younger brother, Jeff, from a friend's house when he accidentally falls into a ravine and is knocked unconscious. When he comes to, he discovers that eight years have passed and it is now 1986. Police are shocked to see David fits exactly the same photo on a missing child poster, having not aged at all. David is reunited with his aged parents and the now 16-year-old Jeff.
Meanwhile, an alien spaceship crashes through power lines and is promptly captured by NASA. David is taken to the hospital for tests, where his brainwaves reveal images of the spaceship. Dr. Louis Faraday, who has been studying it since its arrival, persuades David to come to a NASA research facility for just 48 hours for extra tests, promising him that they can help him learn the truth about what happened to him. There, Dr. Faraday discovers that David's mind is filled with alien technical manuals and star charts covering expanses of the galaxy far exceeding NASA's research. It tells the scientists that he was taken to a planet called Phaelon, 560 light years away, in just over 2.2 hours. They realize that he has experienced severe time dilation as a result of having traveled faster than the speed of light, explaining why eight years have passed on Earth, but not for him. He is unable to comprehend what Dr. Faraday tells him and flees the room, making Dr. Faraday decide to keep David confined to finish his investigation.
The next morning, following a telepathic communication from the spaceship, David secretly boards it and meets its robotic commander, "Trimaxion Drone Ship" (or "Max" for short), which refers to David as the "Navigator". After they escape from the facility, Max tells David that his mission was to travel across the galaxy, collect biological specimens, take them to Phaelon for analysis, and then return them to their homes. Phaelon's scientists discovered humans only use 10% of their brain and, as an experiment, filled the remainder of David's with miscellaneous information. This includes all of the star charts discovered by Phaelon's astronomers, some of which were shown to the NASA scientists during David's interrogation. Max then returned him to Earth, but did not take him back to his own time, having determined that a human would be unlikely to survive a trip back in time. Before leaving Earth, Max accidentally crashed the spaceship, erasing all the computer's star charts and data. Therefore, he needs the information in David's brain to return home.
While Max programs the spaceship for a mind transfer, David is shown the other remaining alien specimens on board, and bonds with a "Puckmaren", a tiny bat-like creature that is the last of his kind after a comet destroyed its planet. Max performs the mind transfer on David to reacquire the star charts, but in the process also contracts human emotional attributes, resulting in Max behaving eccentrically and making goofy laughs. He and David start bickering, and their antics trigger several UFO reports in Tokyo and the US. Meanwhile, NASA intern Carolyn McAdams, who has befriended David, contacts David's family and tells them about his escape in the spaceship; as a result, Dr. Faraday has them confined to the house, and Carolyn is sent back to the facility.
When the spaceship stops at a gas station in the Florida Keys, David calls Jeff and asks him to send a signal to locate their new home, and Jeff sets off fireworks on the rooftop. David and Max arrive at the house, but NASA agents, having tracked the spaceship's every move, get there first. Fearing that he would be institutionalized for life if he remains in 1986, he orders Max to return him to 1978. Max warns this could vaporize David, but David accepts the risk. After the journey back in time, he wakes up in the ravine, walks home, and finds everything as he left it. During the Fourth of July celebration, Jeff is surprised to see the Puckmaren in David's backpack; David tells him to keep it secret while Max flies home across the firework-lit sky, remarking "See you later, navigator!".
Joey Cramer as David Scott Freeman
Paul Reubens (Credited as "Paul Mall") as Voice of Max
Veronica Cartwright as Helen Freeman
Cliff DeYoung as Bill Freeman
Sarah Jessica Parker as Carolyn McAdams
Matt Adler as Jeff Freeman (16 Years Old)
Albie Whitaker as Jeff Freeman (8 Years Old)
Howard Hesseman as Dr. Louis Faraday
Jonathan Sanger as Dr. Carr
Iris Acker as Janet Howard
Richard Liberty as Larry Howard
Raymond Forchion as Detective Banks
Keri Rogers as Jennifer Bradley