Decide what the show will be about. Having a concrete description of the show is vital to getting others interested in the show. Work out the basic storyline and catch of the show. Think of why someone would watch this show, and also why should someone invest in it.
Contact a local public television office. PBS, which is a national public channel, relies on local channels (known as affiliates) to syndicate the shows. There is always a certain amount of national programming as well as local programming, so the schedule isn't always free. But asking to speak with someone involved with programming can't hurt. Also, contacting a local public channel that is unaffiliated with PBS might give you a greater chance of broadcast.
Pitch the story to a producer at the local channel. Remember that public TV stations do not have much money, so the likelihood of getting funding from the station for the show, even if it's a great idea, is low. In fact, the best way to get a chance at the show airing is already having an episode or two filmed to show the producers.