Open the Podcasts app
Tap Library
Find the podcast or episode you want to delete
Swipe left on the episode or show
Tap Delete
Confirm deletion if prompted
To remove downloaded episodes only, open the show and tap Downloaded
Tap the More button next to the episode
Tap Remove Download
To delete all downloaded episodes from a show, open the show
Tap the More button
Tap Remove Downloads
To stop future episodes from downloading, open the show
Tap the More button
Tap Settings
Turn off Automatic Downloads
To remove podcast data from iPhone settings, open Settings
Tap General
Tap iPhone Storage
Tap Podcasts
Tap Delete App or Offload App if available