Broaden your understanding of the basic mythology by going to the bookstore. In addition to companions to the movie set and designs, several novel series, like "The New Jedi Order" and "The Jedi Academy" and "Trilogy" published by Random House and Del Rey, chronicle the exploits of characters linked to the official Star Wars universe.
Join an online Star Wars community. In addition to the official channel sponsored by LucasFilm Ltd., many unofficial clubs throughout the web have detailed information about expanded universe characters.
Get involved in video games. Entirely new storylines are opened up through highly developed roleplaying possibilities as those present in the Knights of the Old Republic series.
Hit up the local comic shop. Many interesting details of the Star Wars university are well documented in some of the comic book series put out by Marvel, Titan and Dark Horse.
Watch the Star Wars cartoons. Series like "Clone Wars" have added a whole new dimension to our understanding of the turbulent time leading up to the formal establishment of the Empire.
Make the distinction between canon and "fanon." There is a lot of information about the Star Wars universe that is actually fan fiction and therefore not an official part of the mythology.