The iTunes Store is host to thousands upon thousands of podcasts, those free audio (and video!) programs put out by everyone from big television networks to a guy in his basement with a microphone.
If you want to see what podcasts are available, click the Podcasts link on the Store's main page. You're then whisked to the Podcasts section, where you can browse shows by category, search for podcast names by keyword (use the Search iTunes Store box), or click around until you find something that sounds good.
Many podcasters produce regular installments of their shows, releasing new episodes as they're ready. You can have iTunes keep a look out for fresh editions of your favorite podcasts and automatically download them. All you have to do is subscribe to the podcast: click the podcast you want, and then click the Subscribe button.
If you want to try out a single podcast, click the Get Episode link near its title to download just that one show. Some attention-needy podcast producers don't give you the single-episode download option; in those cases, you'll see a Subscribe Only link near the title.