Prometheus:
Mankind finally deciphers strange glyphs from various ancient civilizations and discovers that they are some kind of map, pointing to somewhere much further-away than mankind has ever ventured. This implies that life on Earth was somehow "seeded" by an alien race (panspermia:
wiki). Weyland Corp (and Earth collectively) pours most of mankind's resources into building a massive state-of-the-art spacecraft specifically for a journey to the indicated system. They send an elite crew that includes scientists and archaeologists. They arrive on a planet which, I believe, is supposed to be in a system far-beyond the one containing LV-426. It's definitely an entirely-different planet from LV-426; one with an intelligent and advanced space-faring civilization. The Prometheus crew finds something terrifying. I assume they find that the xenomorph is a weapon, intended to wipe-out human kind. A space jockey ship departs the planet with a cargo of leathery eggs (human-adapted xenomorphs).
"It's leaving!"
"Where's it going?"
"Earth."
"If we don't stop it, there won't be any home to go back to!"
Trailers show that Prometheus catches-up with the departed alien spacecraft, then the crew saves humanity and sacrifices themselves by ramming the Prometheus into the alien ship, causing the alien ship to crash onto LV-426. This is the derelict spacecraft that is found in
Alien. [edit: now that I've seen the movie, much of this speculation is confirmed and some of it inaccurate]
Alien:
The Nostromo and crew are basically "space truckers / miners," bringing massive amounts of rare mineral ore back to earth. Missions can take many years. To conserve resources and minimize aging, the crew must stay in stasis during most of the journey to-and-from Earth. The Nostromo is likely many decades old. The mineral ore is sourced so far from Earth that the Nostromo crew cannot communicate with Earth until they have traveled most of the way home. The Nostromo is equipped with an artificial intelligence named "MOTHER." MOTHER's various responsibilities include: overall mission objectives and sub-directives, navigation, keeping track of protocol minutiae, life support, etc. In some ways, MOTHER represents the company and has some amount of authority over the crew. MOTHER's directives include one that requires the crew to investigate any transmission that could be from an intelligent alien life form or another ship in-distress. Some of the crew aren't fully-aware of this requirement, even though it is stated in their contracts. MOTHER handles all vital operations while the crew is in-stasis.
While traveling home with a full load of valuable mineral ore (presumably, after being away from Earth for years). MOTHER detects an artificial beacon coming from a planet LV-426 in a
relatively nearby system (still very, very far from Earth). Without waking the crew from stasis, MOTHER diverts course to take the Nostromo and crew to the system where the signal was detected. This adds many months to the time it will take to return to Earth. When the crew wakes, they initially believe they're nearing Earth. Dallas checks with MOTHER and finds out where they are and why their course was changed.
Bad things happen.
Based on various programming directives and sub-directives, MOTHER decides that the alien specimen must be brought to Earth. Unbeknownst to the rest of the Nostromo crew, Ash is actually an android, fully-beholden to MOTHER and MOTHER's decisions (because MOTHER's authority and decisions represents the company). Ash does everything in his power to ensure that MOTHER's directive is followed; while using the advantage that the rest of the crew doesn't know he's an android and they incorrectly believe he shares the same motivations they do.
More bad things happen. Everyone dies, except for Ripley and her cat. They escape in a "life boat" and drift into space, hoping for enough luck to be picked-up. The Nostromo self-destructs, destroying its valuable cargo of mineral ore. However, the alien was not destroyed and hitched a ride on Ripley's life boat. Ripley has one last encounter with the creature. She blows it into space and toasts it with the life boat's engines...she's left adrift. Ripley and Jonsey go into stasis, hoping against odds to be recovered.
Aliens:
Ripley was lucky, but it took 57 years for someone to find her drifting life boat. Everyone she ever knew is dead. The company has started terraforming and colonizing LV-426, unaware of the derelict spacecraft and its dangerous cargo in a remote area of the planet. The beacon stopped transmitting long before any prospectors or colonists arrived. The company doesn't believe Ripley's story and believes she's covering-up some kind of incompetence that led to the destruction of the Nostromo, the loss of the entire crew, and the loss of the valuable cargo. At this time, the colony has long-range communication technology installed, but it takes weeks for a transmission to arrive, and probably takes a full month to get a response. The company big-wigs demonstrate ignorance about Ripley's story, requiring her to reiterate multiple times that the planet was uninhabited and the crashed spaceship came from some other planet. Just out of curiosity, Carter Burke sends a vague message to the colony asking to investigate the coordinates where Ripley reported finding the derelict spacecraft. No warning or explanation is included. A colonist checks it out, finds the spacecraft, and is brought-back to the colony with a facehugger attached.
Bad things happen.
Carter Burke wants to bring a specimen back, and sabotages the others and their attempts to destroy it.