I mostly find out about movies via getting curious about an actor, or director or producer or editor, style, some element of a movie from something I've seen before and then wikipedia'ing for ages. I'm not necessarily of the auteur school, but once I saw The Passenger I got really into Michelangelo Antonioni and saw lots of his films, and when I saw Solaris it made me curious about Tarkovsky. Other times I'll pick a film style and watch tons of movies in a specific vein, like Nouvelle Vague or Italian Neorealism, or Chinese Wuxia or Hong Kong gangster.
I guess I have a very historical way of looking at films.