Qualifications
If this is the job you want, then you've got your work cut out for you.
First off, you're going to need a college education. Many people interested in becoming art directors in the film industry earn undergraduate degrees in theater, the fine arts (specifically graphic design or interior design, for example), or architecture, and, honestly, these aren't the only majors you could pursue.
There are a number of fields you could study that would be applicable to a career in art direction; the degree you choose to earn is really determined by what set design-related work you want to do prior to winning that "art director" title.
But, whatever you decide to study, make sure you've taken art, interior design, architectural design, and—this is the big one—CAD coursework, because most set design today is done on computers. You should also familiarize yourself with computer programs like Adobe Photoshop and Illustrator, and InDesign.
Many people in the film industry who want to move up and into an art director position go on to earn graduate degrees in production design. A lot of the coursework for this degree has to do with architecture, given that so much of an art director's job involves creating sets. However, you might also find yourself studying illustration, digital design, and storyboarding as part of this degree.
So, here you are, with six years of education under your belt. Is this enough to land you a gig as an art director? Nope, nope, nopitty-nope-nope.
You're going to need years of experience doing set work for plays and/or movies before you can be considered for an art director position in the film industry. Start young—in high school, if you can—and, no matter what happens, never stop working.
It doesn't matter if you're getting paid or if you're a volunteer. It doesn't matter if you're in charge of actually designing sets or if you're doing the grunt work with the props, the backdrops, or the lights. Art directors oversee many different kinds of workers for a film, and so they need to have a keen understanding of everything that goes into creating a set.
So, now you have tons of experience to go along with your extensive education. Is this enough to get you work as an art director? Still a big fat nope.
You see, Hollywood is heavily unionized, and if you aren't a member of the Art Directors Guild—which actually covers production designers, art directors, and every person who might possibly work under them—and if your name isn't on the Motion Picture Industry Experience Roster, then you're going to have a hard time finding a job (source).
Okay. So, now let's say you're very well-educated, experienced, and you're a member of the Art Directors Guild Local 800. Can you be an art director?
Well, maybe. Do you know a guy? Because if you aren't acquainted with a production designer willing to hire you to work on a film, you're going to have a difficult time snagging that "art director" title.