RadioPublic uses storage on your phone when episodes are played or downloaded. Episodes are automatically removed after a period of time once they are heard. You can adjust how this works in your Settings.
To delete the download, tap on an episode and then tap the '...' menu. From this menu you can then tap "Remove download" to delete the downloaded file.
Automatically download episodes from the shows you follow
You can also set things up so the RadioPublic app will automatically download new episodes for you. Typically people enable automatic downloads to ensure new episodes from shows they enjoy are available without having to use their mobile data while not on WiFI. You can adjust how automatic downloads work in the Settings area for the app. You'll want to enable "Download new episodes" which will automatically download new episodes from shows you follow.
Manually download an episode
When viewing an episode you can tap the stacked dots in the menu '...'. From this menu you'll see "Download".