Anchor.fm is one of those easy-to-use podcast creation tools. I featured it in a video in my tip of the week in late February. The folks at Edublogs were kind enough to share it with their followers and include it in their new comprehensive guide to classroom podcasting.
The Edublogger's Guide to Podcasting includes examples of student-created podcasts, examples of teacher-produced podcasts, directions for recording a podcast, and directions for publishing a podcast. And if you are worried about running out of topics for podcast episodes, you don't need worry because The Edublogger's Guide to Podcasting includes 50 ideas for student podcasts.
You can create a podcast with the microphone built into your phone, your laptop, or your tablet. But if you want to improve the sound quality I recommend getting a Blue Designs Snowball iCE microphone (affiliate link). I have two of them that I've lugged all over the world, dropped them from a TSA security checkpoint table, and lent them out to people in my workshops for years. They work as well today as they did the day they were new.