You can integrate your podcasts from plugins like Blubrry Powerpress, Seriously Simple Podcasting, and others.
First, create your podcasts on your site, and setup the AppPresser media urls as described in the video.
Next, use the media list page to add your podcasts, following the instructions here.
Note: the media player and app customizer are outdated in this video, but the process is the same for AppPresser 4.
You can find the code for programatically adding AppPresser media urls here.