Going to film school or studying television production is a great start. The classroom is a great place to learn the professional terminology used in film and television production as well as get some fundamental skills in camera work, sound, lighting and editing.
Getting any job in production can be frustrating. Landing that first job is the toughest. Working for free on a few independent productions is a good way to get a foot in the door and meet people who might help aspiring editors find paying gigs. If any offer comes through, be it an entry level production assistant job or a receptionist job at an advertising agency, don't turn it down. Getting to know people in the industry is key to getting into editing.
Promote yourself. Tell everyone you meet that you want to be an editor. You never know who knows somebody who knows somebody who needs post production help. Turn your production assistant job into a post production assistant job. Take your post P.A. skills and become an assistant editor. Evolve your A.E. skills into becoming an editor. It isn't an overnight metamorphosis but it will happen.
Learn Avid. Buy an Apple Macintosh computer. Install FinalCut Pro. These are industry standards. Avid technology is what most TV shows and films are cut on. It is a platform which is very complex but knowing the basics of how to string out a scene, add music and sound effects, loading footage, making outputs, and other basic skills will set you apart from other wannabes. Almost all Avids are run on Macintosh computers. Get to know how the Mac OS works. If you have a Mac at home, install FinalCut Pro. It is an editing application that is becoming more popular. Frequently you'll see employers seeking FCP editors, and if you've gotten to know the software at home you'll be more comfortable with the job.