I haven't seen much of the Star Wars or Star Trek stuff either, and don't really consider them science fiction as much as space action movies. That's not really what we're talking about.

I would strongly advise you to start with short stories, specifically Isaac Asimov, Robert Heinlein, Arthur C. Clarke, Robert Sheckley, and Philip K. Dick. All those authors are considered giants in the field and have anthologies of collected short stories. Science fiction short stories tend to be easier to read because you don't get bogged down in detail, and you can get right to the point of exploring the interesting and speculative worlds.