From an FAQ at IMDb.com...
How is this related to Ridley Scott's 'Alien' and the rest of the series?
The movie is set in the same fictional universe of Ridley Scott's Alien and has shared events with it, and directly precedes the rest of the original series, but it's definitively not related to Aliens vs Predator. There had been talks of a fifth Alien movie for years, with alternating contributions from James Cameron and Ridley Scott. In fact, Scott had committed to an Alien sequel or prequel several years ago but aborted the project when the studio opted to make the AvP movies first, and both Cameron and Scott, separately, were not supporters of the Alien/Predator crossover series. After the disappointing box office from Aliens vs Predator: Requiem, the studio shelved the AvP series again to go back to the original plan. The prequel film was supposed to cover the origins of the Weyland-Yutani Company.
When the project was initially greenlit, it was seen as two separate movies to be chronologically before the first Alien movie, written by Jon Spaihts, being directed by Carl Erik Rinsc, and Scott staying only as producer. However, Fox wanted Scott in the director's chair so bad that he eventually accepted under the condition that the script was heavily retooled to reflect the concepts that he wanted to explore. Damon Lindelof was the pen to make it happen, and the result has been described in certain moments as a both a prequel and an original story. For instance, in an interview, Michael Fassbender confirmed that this is actually an Alien movie, taking place in the Alien universe. In July 2011, however, Scott stated in another interview that "by the end of the third act you start to realize there's a DNA of the very first Alien, but none of the subsequent [films]".
In short, the story takes place within the same universe albeit not directly connected to the events of the original. There has been some misdirection on part of the film makers to help heighten interest in the film by showing glimpses and links in common with Alien, including imagery inspired by, if not designed and built by, H.R. Giger (Source). The third trailer for Prometheus shows footage of alien spacecraft shaped like the Derelict Ship and the premise to explain the "Space Jockey" inside such ship, confirming that the film does, indeed, take place in the same fictional universe as the previous Alien films, but will focus far more on the Space Jockey race (called "gods and engineers" by Ridley Scott since the early interviews) other than on the so-called "alien creature" or "xenomorph", although a creature does emerge at the end of the movie that looks a lot like the original xenomorph.
More:
Prometheus (2012) - FAQ