Speedpast gives each of your audiodecks its own feed, so your daily sets show up automatically in whatever app you already use for podcasts. (You can also download the sets as audio files to listen in other apps, or listen on the Speedpast website.)
Your feed is private, meaning it's only for you. So it won't appear if you search for it in a podcast app the way a normal public feed would. Instead, you paste your feed's link into your app once, and from then on new sets arrive like any other podcast episodes.
Almost every podcast app can add a feed this way. Look for an option named something like "Add by URL" or "Add by RSS link," then paste in the link for the audiodeck you want to study. Here's how to do that for popular podcast apps:
Open the "File" menu, click "Follow a Show by URL...", and paste in your feed link.
Tap the Library icon at the bottom of the screen, tap the "..." menu at the top right, tap "Follow a Show by URL...", and paste in your feed link.
Tap the + icon, tap "Add URL", and enter your feed link.
Visit your podcast library at music.youtube.com/library/podcasts. Click "Add podcast", then "Add RSS feed", and enter your feed link.
Go to your Library, then Podcasts, tap "Add podcast", tap "Add RSS feed", and enter your feed link.
Go to your Library, then Podcasts (you may have to scroll past "Playlists", "Songs", "Albums", and "Artists"), tap "Add podcast", tap "Add a podcast by RSS feed", and enter your feed link.
If the feed says "Processing" for more than a minute or two, try refreshing.
Spotify is the one popular podcast app that doesn't let you add private feeds, so you can't listen to your Speedpast audiodecks there. If Spotify is your usual app, you'll need a different (free) one just for this — Apple Podcasts works great on iPhone, and YouTube Music works on both Android and iPhone.
Google Podcasts has shut down. Google now points listeners to YouTube Music, which can add private feeds — just follow the YouTube Music steps above.