Last year it was revealed that Google Play Music would get a Podcasts section in 2016, and now we can report that it's already live. For some lucky souls, at least.
The feature will apparently become available for all before the end of this month. Until then, Google seems to be doing some A/B testing on this, but the new functionality is enabled server-side so it isn't part of an update to the Google Play Music app unfortunately.
As you'd expect, a Podcasts entry shows up in the app's side menu, under Music library and above Browse stations. Once you tap on that you're taken to the new section, that comes with two tabs - Featured and Your podcasts. A search bar is at the top, naturally.
When you decide to subscribe to a podcast, you're asked if you want to download the latest five episodes and get notified when new ones get released. The Now playing screen for podcasts is similar to the one used for music, save for one difference - the thumbs up and down buttons have been replaced with ones that let you skip 30 seconds forward and backward, respectively.