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.
If you are having trouble with an episode in the Shows section, you can also locate it under the "Daily Feed Plus" icon, which lists all Plus podcasts by release date.

*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