Deleting any playlist is easy (perhaps, for some, too easy)
At the top of the playlists page select "Edit"
Red circles with a horizontal white bar appear beside each playlist title.
Select the red circle next to the list you want to delete,
"delete" appears. Touch delete.
Touch "done" at the top to leave the edit page.
Or
In the playlist menu, left-swipe on a title, then touch delete.
Take care, you have a choice: just remove the playlist OR delete the platlist AND THE SONGS IN IT which will also delete the songs from your library as well as any other playlists you may have placed them in.