The crew of the Nostromo awakens from hypersleep and is informed by the ship's computer Mother (because that's not Freudian or anything) that they have been rerouted to a tiny, unexplored planetoid to investigate a signal of unknown origins.
Does that sound like a bad idea? Sure does.
But the crew's contract states that not investigating means they must forfeit their paychecks. Onward.
The Nostromo lands on the planetoid but is damaged during the process. Crew members Dallas, Lambert, and Kane go out to investigate the signal while the rest of the crew stays behind to make repairs and serve as support. The away team discovers a crashed alien ship like nothing they've ever seen before. Inside, they find the corpse of an alien and a cave-like room filled with giant leathery eggs. Kane pulls a redshirt move and decides to investigate one of the eggs.
Because it's sci-fi, he is promptly attacked by some creature.
Yeah, we all saw that coming.
Back at the ship, Ash tries to remove the creature from his face, but acid blood and the wee beastie's temperamental personality prevent him from doing so. Eventually, the thing simply lets go and dies. Kane survives with a sore throat but seems otherwise unharmed.
So we're all good, right? Yeah, let's eat.
The crew sits down for a final meal before going into hypersleep, but guess who's coming to dinner? Hint: It's not Sidney Poitier. An alien bursts forth out of Kane's chest, killing him. The crew decides they won't be able to hypersleep soundly with that thing on board, so they go a-huntin'.
As we enter the horror half of the film, Brett and Dallas fall victim to the alien, and Ripley discovers the Company actually sent Ash to ensure the alien's retrieval. Ash attacks Ripley, but Parker and Lambert fight him off, revealing him to be an android. They plug Ash back in to ask him how to kill the creature, but hahaha (says Ash) they can't. They are fighting the perfect organism.
Ripley decides enough of this noise. They'll escape on the shuttle and blow up the ship. Ripley preps the shuttle and goes looking for Jonesy, while Lambert and Parker gather coolant for the journey. With the terrible timing of any true movie monster, the alien arrives to kill both Parker and Lambert.
And then there was one.
Ripley sets the self-destruct on the ship, escapes in the shuttle, and watches as they ship and alien are blown into space dust.
The alien managed to escape on the shuttle with Ripley. Doing some quick thinking, Ripley slips into a spacesuit, straps herself into a seat, and blasts the creature into space. When it attempts to crawl back into the shuttle through an engine, she hits the throttle and blows the creature away.
The end—for reals this time. Ripley enters a log into the computer relating the fates of the Nostromo and its crew. The final shot is of Ripley and Jonesy in hypersleep as the shuttle drifts through space.