(Introduce yourself. Something like this: Hi, I'm (insert your name here) and you can hear me on (station) at (time you are on the air.))
(Give some background information about your personal life that is clever and relevant. Tell them about what movies you like, tailoring your answer to the station you are on. In other words, if you're on a news station, pick something like that Edward R. Murrow flick from a few years ago; if you're on a classic rock station, say “The Wall,” or “Hair” or something like that. Mention what kind of music you like (hint: It's whatever music the station you are on plays), favorite foods (pizza is safe and non-controversial), and what you like to do when you're not on the air. Try to make it more interesting than your actual life.)
(Insert information about your career; where you've worked, how you got to the station you're at, that kind of thing. Feel free to make it up; what are they going to do, check?)
(Make some local references that show you're attached to the community you're now working in, even if you just got to town, or are recording your show from far away. Find out which roads have the worst traffic problems and bemoan it; mention liking some local sports team(s). It never hurts to say what you love best about (whatever area you are in) is "the people").
(Here you could do a Q&A kind of thing, where you answer questions from listeners. No questions from actual listeners? No problem! Make some up!)
(Close by mentioning how excited you are to be working at whatever station you are at, and invite the reader to tune in frequently. Perhaps mention that they can make a request and give the phone number, unless you don't do your show live or are from out of the market, in which case you could give your email address. Don't worry about that tipping them off that you aren't actually there doing your show when they are listening; the listeners don't give a damn about you or your station. That's why they just read several hundred words about you.)