The way my first partner and I did it was to bring the station a video of a tornado. Our first chase yielded a tornado that no one else had seen, and the station was so impressed by our obscure catch, they offered us a gig. We had chased once in our lives, and were given jobs chasing for the number one station in the world for covering severe weather, KWTV-9 in Oklahoma City. But as with everything involving me and chasing, this was hardly the normal way things happen.
I really don't know how to go about chasing for a TV station, except to show up in their lobby everyday, drink their coffee, showing them how persistant you can be and how much it means to you.
Good luck.