Qualifications
Anyone can be a TV writer, but not everyone has the determination to stick out the lifestyle, learn the craft, and work in a collaborative environment. You also have to have stories that need to be told. What's so interesting about you and your experiences? What's your voice as a writer? How is your story different and how will you tell it? These are all questions to ask when deciding to pursue the career path of a TV writer. Storytelling must be your passion and first love (of the non-human variety, that is).
Writers have a variety of academic experience. Some have just graduated from high school, but most have gone to college. There are even some who have graduate-level degrees, which are great, but not necessarily required. There is not a specialized degree needed in order to pursue TV writing, which can be both exciting and a little frustrating.
You can major in marine biology and still be a TV writer. In fact, a degree in marine biology could be a great asset if you end up on a one-hour murder mystery about a dolphin trainer. The point being, having knowledge of a specialized area can actually help you get a job. The more varied your life experiences—education included—the more versatile you'll be as a writer.
Some writers choose to go to grad school and get their MFAs, but an education in screenwriting is not necessary. It doesn't hurt, but you can also learn the art of screenwriting by purchasing books and Final Draft, the primary screenwriting software used by all feature and TV writers.