A showing of The Rocky Horror Picture Show is different from everything else you have seen. If you are open minded and if you love cinema, you should watch it as soon as you have a chance. You don't need to know anything about the movie (you really shouldn't in my opinion, that's part of the magic), just don't watch it at home.
The movie was a box office failure in the U.S. in 1975. The producer, Lou Adler, decided to move it to the midnight movie circuit in 1976 to try to get some of the investment back. That was when the cult began.
At first, the movie was a success among the transvestite community and science fiction fans, but then it got out to the general public and became a national sensation. It is hard to explain why it happened, but the snowball effect is easy to understand: you are watching a movie with a crowd of people dressed up exactly like the characters, who know every single line in the script and each time there is a more questionable quote they shout back at the screen with a witty comment or a sexual joke. So it can happen pretty much anything.
I probably didn't answer your questions, but the fact is there isn't an straight answer to the why, what or how. You will understand everything after you go out and watch a night session of The Rocky Horror Picture Show.
Edit just to add a few things about the movie itself. This is a musical/comedy. It's a tribute to classical science fiction movies and, at the same time, it carries a strong message about liberty and about exploring the limits of one's sexuality. It has a brilliant soundtrack and a simple (almost naive) humor. Whether live or at home this is not a movie that everyone will enjoy. Not everyone enjoys musicals, not everyone will laugh (specially if you are watching it alone) and the sexual content may be a little too much for some people. Nevertheless, it is a unique live experience.