As to how one find them, I have a number of strategies:
First and best is to find people who share your taste and ask them for recommendations.
Second, find other films by the directors and writers who's films you like.
Third, read reviewers, forums, blogs, and magazines that talk about your favorite genre of films.
Fourth, try doing web searches for more than one of your favorite films at a time. If you get lucky, you might find them all on a list of great movies and go from there.
Fifth, there used to be a website called YMDB (if I'm remembering right), which used to let you put in your top 20 films and match you up with others who had similar tastes, and then you could see what other movies they liked. Unfortunately, it's no longer around, and I'm not sure if there are any other services like it these days.
Sixth, find lists of great movies and watch as many of them as possible.
Seventh, go to movie clubs and art house cinema houses and watch what they show or maybe talk to some of the people there and see what they can recommend given your taste in films.
Eighth, read some books on film.
Ninth, listen to directors' commentaries on the movies you like, and read interviews with them. They'll often mention films and directors that influenced them. Watch those.
Tenth, rate all the movies you've seen on dvd.netflix.com and then look at what they recommend based on your ratings.
I've long been a pretty avid film watcher, including of classic films, but my tastes are pretty mainstream. If you're looking for new views, I'd just suggest Googling using terms like "Most underappreciated science fiction films" and things like that. Some good channels on YouTube as well.
I like science fiction and well done period dramas (i.e. historical fiction or alternative history). I am not really into high-brow art movies, as I don't really have the education to get them. Is there really a wide world beyond Hollywood for the type of movies I enjoy? If yes, how does one go about exploring this world?