If you have yet to see the Podcasts section show up in your Google Play Music app, a simple tap on the “Refresh” button in settings should force it to arrive. Seriously, just pop into your app, slide out the side navigation menu, tap on Settings and then “Refresh” and you should then see the option for Podcasts just under Music Library.
This same trick worked for the family plan when it arrived as well.
If that trick doesn’t work, then maybe you need to update your Google Play Music app first. You can grab the newest version here (v6.7.2712Z.2783167).
Also, have you subscribed to the Droid Life Show through Google Play Music, yet? You can right here.