You just connect via Bluetooth and use whatever podcast app on your phone you want to use. The bluetooth functionality on my MY is very good (much better than my Ford with SYNC). My only complaint is a slight delay between pushing a button to skip/pause and it actually happening (about a second or so), but otherwise it's great.
Personally I like the Overcast app on my iPhone, but anything will work, including Apple's default Podcast app. For music I switched to Tidal because of the high quality streaming (Spotify isn't great and Apple Music is even worse), and because they have higher artist payouts, and other than not having a Shuffle function in the car (WTF?) I have no issues with Tidal and I actually really like the mixes that it creates for you.