Sign in to the app with your Slate Plus account (more info here)
Select the Headphones icon in the top right corner. You may need to wait for the page to load.
To find a list of episodes grouped by show, select "Shows" at the top of the page.
*Please note that though the episode timestamp may display the shorter length at first, when loaded the podcast will play the full extended Plus version.
To learn more about accessing your Slate Plus podcast benefits outside of the Slate iOS app, in the podcast player of your choice, follow the instructions here.