Instructions

Apple Podcasts on Mac (iTunes on Windows)
Click on "File" in the top left menu. Then select "Add a Show by URL..." from the dropdown and paste the feed URL in the pop-up window. Click "Subscribe" and voila! 

Apple Podcasts on iOS
Tap "Library" on the bottom row of icons. Then hit "Edit" on the top right, and select "Add a Show by URL...". Then paste the feed URL and tap "Subscribe" and you're off to the races. You can also use the instructions at the link below.

https://www.imore.com/how-add-podcast-url

Pocket Casts (iOS, Android & Web)
Paste the URL of the feed into the search field in the "Discover" tab and then hit search. Tap on the podcast that should appear in search results and then mash that "Subscribe" button.

Breaker (iOS & Android)
Tap the "Library" tab, then select the "Subscriptions" tab. Tap the "+" in the upper right and select "Add from link". Paste the feed URL and tap done!

Overcast (iOS & Web)
Tap the "+" button in the top right like you normally would to add a podcast. Then select "Add URL" in the top right, paste the feed URL and hit done!

Castbox (iOS & Android)
Paste the feed URL into the search bar at the top of the "Discover" tab and then hit search. Then hit "Subscribe" and you're done.

Podcast Addict (Android)
Tap the "+" icon in the top right. Then it'll take you to the "New Podcast" screen. Then there is a second "+" button you'll need to hit before selecting "RSS feed". Then paste in the feed URL and tap "Add." to finish.

On the main screen you click the + (top right) and it takes you to the "New Podcast" screen. Then there is a second + button that takes you to options including "RSS feed, ...". Click that, add the "RSS feed URL," click "add," and blastoff!

Downcast (iOS & Mac)
Tap "Add" on the bottom bar, press "Add Podcast Manually" and in the "Feed" field paste the URL of the RSS feed. Then hit "Subscribe" in the top right.

Podcast apps that *do not* support manual RSS
As of October 2019, it is not possible to manually add an RSS feed to Spotify, Google Podcasts, Stitcher or iHeartRadio

 

If you need more instructions for an app not listed here, just search for "[name of podcast app] add with URL."