My belief that podcasts could be effective in the classroom came from my own enjoyment of podcasts like NPR Selected Shorts and New Yorker Fiction. Try subscribing to a few podcasts (download iTunes for free if you haven't already). If you're inclined to be suspicious of educational claims involving new technology, check out iTunes U, where you can find thousands of recorded lectures on everything from classical sculpture to Mid-East politics.
Ask your friends whether they listen to podcasts or audiobooks, and what they like. Talk to people in your department. I found out that David Arendale, two doors down, has been using podcasts to teach U.S. and global history for eight years! He loves the tech side and has in his office a mini recording studio that students use to produce their own programs. I walk right by Dave's door ten times a day, and I never knew this. Invite an IT person into your office to shoot the breeze. There's no reason to wait until you have a specific technical problem. If you explain you budding, even tentative, interest in using podcasts, chances are this person will offer a handful of easy tips and help you find resources you didn't know existed.