Many people who work in the broadcast industry have studied broadcasting in college. Not all of them have completed those programs, but it's definitely a good idea to have a college degree if you want to enter that field. On the other hand, there are broadcasters (in radio especially) who didn't have formal training in college, but were able to start in a low level position at a radio station, usually as an intern, and work their way up. While I didn't start as an intern, I didn't have any formal broadcast training when I entered the radio business. I did, however, have audio production skills (most of which I learned on my own, starting while I was in middle and high school). Those skills allowed me to get a job as a production director at a local station, which eventually led me to moving up into more prominent positions including as an on-air talent (radio DJ).
If you're serious about broadcasting, I would suggest going to a college that offers broadcasting or radio/TV programs, get yourself onto the college radio station, and seek out internships at commercial radio or TV stations in your area.