Sign in to the app with your Slate Plus account (more info here)
Select the Menu icon from the main screen (three parallel lines), then select Podcasts. Then tap Shows.
Tap the show you want to listen to, then tap the Slate logo under "Get your ad-free Slate Plus podcast:"
This will open a new window inside the app. On that page, you can tap to subscribe and listen to the show
in the podcast player of your choice; just follow the instructions here.
You can also choose to listen to an individual episode inside of this new window. Tap on an episode name to go to that episode and use the audio player on the page. Please note: this player cannot keep track of your position in the episode if you close and re-open the app. For the best listening experience, follow the instructions above to subscribe to your favorite shows in your preferred podcast player.