On February 20, 1963, a young girl named Andie (Hollye Rebecca Suggs) is laying out under the stars somewhere in the rural farmlands of America, trying to see if she can spot Friendship 7 during its return to Earth after its historic orbital mission. She noticed what looks like a shooting star, which blinks in the sky. Taking this as John Glenn winking at her, Andie promises herself that, one day, she too will become an astronaut. 23 years later, Andie Bergstrom (Kate Capshaw) flies a T-38 Talon into John F.
Kennedy Space Center and meets her husband, fellow astronaut and former moonwalker Zack Bergstrom (Tom Skeritt) on the tarmac. She is now in NASA's astronaut program, but has not flown into space yet. In fact, she's upset that she was passed up for a coming mission. Zack immediately cashes in on a promise she made if she didn't get the flight: he recruits her as an instructor for that summer's Space Camp program.
As registration begins, among the arrivals for the program is Kevin Donaldson (Tate Donovan), driving his new Jeep. Initially he rubs Zack the wrong way by parking in his spot. After he moves his Jeep, he notices the young female pilot of a biplane flying in: Kathryn Fairly (Lea Thompson). Immediately smitten, he catches up behind her in the registration line. Wanting to get closer to her, he steals somebody else's credentials so he can end up in the Blue Team, the same team as her. As it so happens, the Blue Team is the one being instructed by Andie Bergstrom, whom Kathryn idolizes as one of the few female pilots in the shuttle program. She realises that Donaldson is not on her list of students, but as Hideo Takamini (Scott Holcomb) isn't around, she just lets things be.
In addition to Kathryn and Kevin, three others make up the team. Tish Ambrosei (Kelly Preston) has the look of a valley girl, but is highly intelligent, with a photographic memory and a perfect SAT score. Rudy Tyler (Larry B. Scott) is a young African American man from a military family; he loves science, but isn't very good at it. Last, there's Max Graham (Joaquin Phoenix), a kid with a Star Wars obsession that is still young enough for the junior program. Andie permits Max on the team since he's been in the junior program for the past two years. Andie gives shuttle positions to each of the cadets.
To everyone's surprise, the seemingly irresponsible Kevin is made Shuttle Commander, while Kathryn, who aspires to be a real Commander one day, is named the Pilot. The others are Mission Specialists. Tish is responsible for communications, while Rudy is responsible for operations. Max is not given a specific area of responsibility. During the initial tour, the Blue Team is introduced to a "prototype maintenance droid", a robot called "Jinx" (Frank Welker's voice).
He was intended for use on a future space station, but too many bugs in his AI programming relegated him to service work around the Cape. Max hides Jinx in his closet. One night, Jinx is teased by other members of the Space Camp, particularly the Green Team, who ask him to do twenty things at the same time, resulting in frying his circuitry. Max spends the night repairing Jinx, and the two become, as Jinx says, "friends forever". For the Blue Team, Space Camp is anything but smooth sailing. Although they develop a camraderie together, they have difficulties working together as a team, largely the result of Kevin not taking his position as Commander seriously.
Kathryn, in addition, is frustrated by her inability to master the multi-axis trainer, a prerequisite for any real shuttle pilot. Kevin succeeds in bonding with Kathryn, and gets directions from Jinx to a good place to see the Space Shuttle, Atlantis, on the pad so he can sneak out with her. Unfortunately, Jinx readily rats them out to Zack when they turn up missing. Kevin blames Max for Jinx's betrayal, leading Max to wish aloud, while wandering the camp alone, that he were in space. Overhearing him, Jinx takes it literally and works with other NASA computers to figure out a way to get Max into space.
Meanwhile, Andie and Kathryn had the opportunity of having a chat together: Andie complais that Kathryn is much more tougher on her than on the rest, and Kathryn reminds her that she will only be able to command a shuttle if she is best than all the others. Tensions in the Blue Team come to a head when they end up screwing up in a simulation. The Green Team arranges for the electric power to create a circuit malfunction. Kevin didn't take the situation seriously, Tish and Rudy argued about what do; Kathryn left her place as pilot to go and argue some more with Rudy and Tish.
All this happening while Max is left outside on the outer arm, being jarred repeatedly and getting dizzy. All this led to disaster: if there had been a real-life situation, they all would have died. While Kevin doesn't think it's a big deal, Andie has to lecture him on responsibility. The Blue Team earns a once-in-a-lifetime opportunity: they will sit in Atlantis during a test firing of its main engines. This gives Jinx his chance. During the test, Jinx orders a computer to send a code to Launch Control: a "thermal curtain failure" in one of the solid rocket boosters. Unlike the main engines, which can be turned off, the solid rockets cannot be stopped once lit, essentially requiring Atlantis to be launched.
Atlantis, with the Blue Team on-board, successfully reaches orbit. However, they have two problems, both caused by the fact that Atlantis was not yet equipped for an actual launch. It does not have its normal communications equipment installed, and it only carries 12 hours worth of oxygen. They do not have enough oxygen to get to the next available window, or opportunity, to safely land at Edwards Air Force Base, the normal Shuttle Landing facility. Unable to communicate directly, with only telemetry relaying between the ground and Atlantis, Launch Control director (Terry O'Quinn) and the Blue Team both think of how to get more oxygen and get home. Andie remembers something: Space Station Daedalus, under construction but already carrying extra oxygen canisters. They could recharge their own oxygen tanks there.
During the transit to Daedalus, Tish begins to use one of the telemetry switches, the "CXT switch", to attempt to reach Launch Control via Morse code. When they reach Daedalus, Andie begins a dangerous solo spacewalk to get an oxygen tank from the space station. However, she is too big to reach any of the tanks through the station's truss structure. Max agrees to go out, in a suit scrunched down to his smaller size by one of Tish's belts, and he successfully grabs two tanks; one for a backup. Before they get back to Atlantis, Max accidentally ends up hurtling away from the space station, but Andie uses her manned manuevering unit to catch up to him and bring him back safely. During the misadventure, Atlantis runs out of oxygen reserves, leaving those inside with just the air in the cabin. When Andie goes to fill the tanks, there is a problem. She cannot decide which of the four tanks needs to be filled first.
Rudy and Kathryn each have a different choice. There are four valves: from left to right, a single-headed blue valve, a red valve, a yellow valve and a double-headed blue valve. They must be filled in the proper sequence. Rudy thinks it's the blue valve next to the yellow, while Kathryn thinks it's the blue valve next to the red. Rudy tells Andie to go for the one next to the yellow valve. It works. The tank is emptied completely into Atlantis, buying them 12 extra hours on orbit if necessary. Finding out that Atlantis has more oxygen via telemetry, Launch Control puts the shuttle on auto, so it will take the next available window to landing.
However, Andie connects the second tank to the second head on the double-headed blue valve instead of going to the yellow valve, and blows the tank off of the connection, sending her hurtling into the back of the payload bay. Andie is left unconscious, seriously injured, and floating slowly out to space. Max tries to pull her in by her lifeline, but the payload bay doors close, pinning Andie outside of Atlantis. Kevin makes a choice: he overrides the auto landing, missing the window for Edwards AFB, and reopens the payload bay doors, bringing Andie back inside Atlantis.
The Blue Team immediately explores other options to get home, as they again do not have enough oxygen to get to the next window for Edwards AFB, and don't have enough air left in the space suits to return for more oxygen at Daedalus. They begin to explore other places to land, and figure something out: White Sands Missile Range, New Mexico, where Columbia had to land at the end of STS-3. Just as they begin their preparations, Jinx, who has discovered Tish's Morse code, reaches Launch Control and brings the contact to Zack's attention. NASA finally acknowledges the Blue Team, and quickly learns the full situation. Andie wakes up, but is still hurt badly, and it's up to Kevin, Kathryn, Tish, Rudy and Max to land Atlantis. Kathryn takes the role of pilot, just as in Space Camp. It's then that her worst fear comes to pass: Atlantis enters a flat spin after its deorbit burn, exactly the situation that the multi-axis trainer simulates.
Kathryn manages to regain control of Atlantis. After a tough manual reentry, Atlantis makes it safely to a landing at White Sands..