I don't have any personal experience running a podcast, but I've been a big fan of the medium since it reached critical mass. These days, most of the podcasts I listen to make money with advertising inserted into the feed, often read by the hosts.
For those who listen to a lot of podcasts, there are a few usual suspects who tend to appear across a wide variety of subjects. I'm looking at Mailchimp and Squarespace
I'm sure there are other ways to monetise podcasts as well. Bigger operations, such as Gimlet Media, have ventured into producing entire podcasts series as a way of branding and content marketing. While we're on the subject of Gimlet, I would highly recommend listening to the first season of their inaugural podcast StartUp. It's not only a marker for the medium, it chronicles the process of starting a podcasting company!