Lights, camera, action!
After destroying the Death Star, the Rebel Alliance is forced to hole up on the freezing planet of Hoth while the Empire desperately tries to locate their secret base. In fact, the movie starts off with an Imperial probe crash-landing onto Hoth's surface.
We knew it was gonna be good.
The whole thing is witnessed by Luke Skywalker, who's performing recon. Before he can investigate further, however, he's attacked by a space yeti (a.k.a., a wampa) and dragged to its cave. Luckily, Luke manages to break free using his telekinetic Force powers and shiny lightsaber. In a daze, he has a strange vision of his now-dead mentor Obi-Wan telling him to go to the planet of Dagobah to learn from his former Jedi master, Yoda
Meanwhile, Luke's pal Han Solo is getting worried. Not just about Luke, either; he has a price on his head from the crime-lord Jabba the Hutt and needs to leave to make things right. He also desperately wants Leia to admit her feelings for him, but she continually refuses. (Apparently she didn't realize he's Harrison freakin' Ford.)
Regardless, Han goes out to rescue his friend, and they make it back to base safely the next morning.
That doesn't last long: the Empire is currently preparing an assault on Hoth. Luke jumps into a ship to fight the Imperial ground forces and buy time for the evacuation before escaping himself: Luke heads to Dagobah, while Leia joins Han & Co. on the Millennium Falcon. Oh, and the Empire's nipping at their heels the whole time.
From here, our heroes diverge. Luke makes it to Dagobah and meets Yoda, who agrees to teach Luke despite his better judgment. At one point, Luke enters a cave to find a hallucinatory Darth Vader, whom he decapitates only to reveal Luke's own face underneath the helmet.
In other words, Jedi training is pretty psychologically taxing.
Han and Leia, on the other hand, hole up in an asteroid cave to evade the Imperials. There they grow a little closer and even kiss briefly—awww—but after the cave turns out to be the belly of a giant space worm (yes, really), they decide to go to Cloud City, a small mining community on the planet Bespin. The boss there is a guy named Lando Calrissian, an old buddy of Han.
Everything seems swell at first: Lando has a great mustache and he's a charming fellow. Then, after inviting them to dinner one night, he reveals that they'll have an additional guest.
Yep. Darth Vader. It's a trap! Not for Han and Leia, though; it's a trap meant to snag Luke.
It works like a charm.
Luke has a premonition of his friends in danger and decides to end his training early to rescue them. Yoda vehemently opposes this, saying that Luke risks falling prey to the dark side, much like Vader, who was once Obi-Wan's apprentice. Still, Luke is too concerned with his friends to even consider staying.
Meanwhile, Han's body is frozen in carbonite so a bounty hunter named Boba Fett can bring him to Jabba the Hutt. Luckily, Leia and Han share some "I love yous" (well, kind of) before it goes down. Vader then breaks his promise to Lando that Leia will be free to go and orders her instead to be brought to his ship.
Now this is where things get juicy.
Lando abruptly switches sides once again, turning the people of Cloud City against the Imperials and freeing Leia. They manage to get to the Falcon safely. Meanwhile, Luke has arrived in Cloud City and is approaching the red-lit carbonation chamber where Han was frozen. Suddenly, Vader appears and—bam—we've got a lightsaber duel.
Vader handily wins the fight, slicing off Luke's lightsaber-swinging hand and pushing him to the end of a balcony. Then he drops a mega-bombshell—he's Luke's father. Cue a melodramatic "No!" and Luke throwing himself off the balcony. Luckily, he manages to grab hold of an antenna hanging from the bottom of the city and telepathically contacts Leia (wait, what?) to pick him up in the Falcon.
After escaping the Imperial forces, our heroes reunite with the rest of the Rebels. Luke even gets a brand new hand. Meanwhile, Lando has been preparing the Falcon for a rescue mission for Han, which will kick off the next and final film in the original Star Wars trilogy: Return of the Jedi.