If you have students who create their own music or produce their own podcasts, your can use SoundCloud or PodOmatic to publish them on the Internet for free. Both websites offer free accounts that can manage a load of material without dropping any cash. The Slides below will walk you through the basics of publishing a podcast on each website. Youtube is another option, but I prefer SoundCloud and PodOmatic because they are specific for the task of sharing music or podcasts; Youtube is great, but video content is more the focus of the website. I've encouraged students to do podcasting in a number of ways, but my personal favorites have been when they promote their own music or opinions and learn to use social media to spread their content.
In my Presentation and Performance course, I would make podcasting like a journal assignment in my English courses. The idea was that each student published five episodes a semester and each episode was two to three minutes long. I left the content up to them, but I did require them to promote the podcast. Students were require to visit each other's podcasts and leave at least one comment for all of their classmates during the semester. Most of the students loved it. They had freedom with regard to content so they were interested in making episodes and promoting them. One student produced his own version of Car Talk; one student made videos of her singing her favorite songs and challenged others to make their own versions of the songs; and another student demonstrated different styles and techniques in applying cosmetics. One of the biggest benefits for students, other than learning how to make podcasts, was their appreciation for the sound of their own voices. A person sounds very different when recorded and played back and it gave students an opportunity to work on voice quality and control in a non-threatening way.