David Scott Freeman (Joey Cramer) is an average, twelve-year-old American boy living in Fort Lauderdale, Florida in 1978, who owns a young dog name Bruiser whom he tries to teach Frisbee tricks. On the night of July 4, his parents (Veronica Cartwright and Cliff DeYoung) ask him to go retrieve his younger brother Jeff (Albie Whitaker) from a friend's house, which is located on the other side of the woods that are behind his house. While in the woods, David falls down an embankment into a ravine and is knocked unconscious. He awakes after what seems like a few moments. He returns home, only to find that he is now in the year 1986 and that everything has changed but himself. His childhood home has been sold to a married couple, who believe David is a missing child and report him to the local police. The police do not understand why David, who has been declared legally dead after being missing for so long, still looks the same as when he was last sighted. They are further puzzled when they start asking David questions and when asked who is the current President of the United States, he answers with Jimmy Carter. The police take David to a house where he is reunited with his family, now aged 8 years.
Meanwhile, an extraterrestrial spacecraft has crashed into some power lines. NASA agents convince the police that the craft is theirs and take it to their base, intending to study it. The NASA workers find the ship seamless and impenetrable.
David is taken to the hospital to try to determine where he has been for the last eight years, and to discover the reason for which he has not aged. The scientists have begun performing tests on his brain and find it to contain accurate information pertinent to the alien spacecraft that is at the NASA base; further scans reveal that his brain contains alien data and star charts leading to the planet of Phaelon, which is such a great distance away NASA had not charted it. This planet is described as being exactly 560 light-years away from Earth. The travel time used by the spacecraft to reach it is 2.2 solar hours, implying a speed of approximately 2.25 million times the speed of light. The concept of time dilation is therefore used to explain the fact that David has not aged and is unaware of more than a few hours' passage.
David befriends an intern named Carolyn McAdams (Sarah Jessica Parker), telling her to let his parents know that the institute plans to keep him longer than the promised 48 hours. David hears the ship calling to him telepathically. He escapes the room by hiding in a service robot called RALF. Ignored by security, this robot takes David to the hangar where the ship is stored. As if made of liquid metal, an opening and stairway appear on the underside of the hovering spacecraft, and David climbs inside. Once inside the ship, he meets its robotic pilot, whom he subsequently nicknames Max (voiced by Paul Reubens). Referring to David as "Navigator", Max accepts David's command to escape the base and take him somewhere to think.
The ship takes off from the NASA facility and hides on the ocean floor of the Gulf of Mexico. To travel more quickly, Max causes the spaceship to morph into a streamlined, point-nosed form designed to penetrate thicker atmosphere than that of Phaelon. The craft shows the abilities to hover, to accelerate at high G, to travel at tremendous speeds (up to Mach 10, or ten times the speed of sound), to become transparent, to travel underwater, and to move in virtually any direction without any discernable engine or power source.