Tap on playlist to focus on it. Use buttons in the bottom to edit or delete.
Double tap to play playlist.

Melody icon: currently playing.
Transparent background: focus.
Tap on back button in right top corner to return to song list.

upd:
Edit menu will open the similar to mockup window with Playlist name instead of title "Playlists" (tap on it to rename) and songs instead of playlist #1, RHCP, etc.
Buttons: add (submenu: folder, folder with subfolders, single file), delete (long tap to delete song from harddrive)