Let's get the obvious out of the way first: yes, Prometheus is definitely part of the Alien franchise. Coming from the man who gave us the original film in 1979, we would expect no less. Some viewers are going to be miffed that the film takes so long to get to the connection, but that is part of the journey. This film is definitely as much about the getting there as being in the moment of awareness. You're going to either love or hate that depending on your appreciation of the film maker's craft.
This highly anticipated film is extremely well-crafted. You can see the artisan's attention to detail in every frame. This is something I learned from Ingmar Bergman's philosophy of film; each frame should be an individual image that is like the painting of a great artist. You can see Scott achieving that here, from the opening on bubbling and erupting new earth, to the twisted rocks of the alien planet, to the interiors of the ship Prometheus and the alien lair.
The story centers on Dr. Elizabeth Shaw (a luminous Noomi Rapace), a cross wearing scientist who along with her colleague (and beau) Charlie Holloway (Logan Marshall-Green), convinces zillionaire Peter Weyland (Guy Pearce) to fund their project into outer space based on cave drawings found around the world. The logic is that all these similar drawings point to one planetary system, and from here the "engineers" came to earth and helped create human life. The fact that Weyland is old and dying motivates him to seek the origin of the species, with a hidden agenda (as in all Alien films) that we discover later on.
Other important characters are David (played impeccably by Michael Fassbender), an android who is Weyland's right hand "man" on board, Meredith Vickers (an icy Charlize Theron) who is the company representative who comes along to make sure things go according to plan (again, being an Alien film, the plan itself is dubious from the start), and Janek (Idris Elba) the ship captain who references Stephen Stills and decorates a Christmas tree. This little moment seems insignificant as Shaw's cross, but it comes to represent much more later in the film.
It is difficult not to give away spoilers here, so let it suffice to say that Shaw and company should have remembered the old "Be careful what you wish for" saying. They are looking for origins (one character even mentions Darwin) and when they find something to prove their thesis (the engineers in question have human DNA) it is not enough. When Charlie tries to tell Shaw that she should stop wearing the cross because of finding the engineers, Shaw explains that she chooses to believe because someone had to make them too.