As Michelle said, this industry is very tough to get into but that shouldn't discourage you by any means. It takes more than just skill but also a lot of drive and determination and the ability to stay positive. Getting an education from a film program cannot hurt in any way and that list provided by Michelle has the best schools but even if you don't go to one of those programs you can still break into the business (I went to a college not on that list and was able to find TV work within my first month of graduating).
As for becoming a director, you will want to learn all areas of production as possible. Start creating short films as soon as possible. The top film major who graduated alongside of me started making parody videos on youtube his freshman year, and upon graduating received a writing job for one of the late night talk show hosts. Learning how to edit, write, and produce will also go along way for your career as you will better understand all the areas that go into telling a story on screen. Also get involved in any clubs and organizations that involve production or storytelling. The best film majors in my program worked on the school TV station, were part of an improv troupe, or a member of the film society. Surround yourself with creative individuals and keep practicing and you will do great.