It's true that deleting a Playlist from and iOS device will also delete the playlist from iTunes. However that does not delete the music from the cloud, nor, in my experience does deleting the playlist actually delete the music downloaded to the iDevice. I suggest that so see just the music that has been downloaded to the iDevice you go to Settings > Music and set "show all music" to OFF. This will display only the tracks that have been downloaded to your iDevice.
As to how to delete music... you can simply swipe across individual songs and tap delete. Or tap-n-hold on any Album or Artist and tape the "x" to delete. It is possible to delete all music from the iDevice by going to Settings > General > Usage and tapping Music, then swiping across and tapping the delete button.
Thanks for the tip regarding the music delete - I was able to remove everything from my iPhone to free up some space.
I have two lingering questions:
1) how to refresh the playlists - for example, I had one playlist that I hit "clear" on earlier that doesn't show any music on my iPhone, but is still in my iTunes. I figure there is something completely obvious that I'm missing.
2) Similarly, I have a playlist with 207 songs that show as matched or uploaded in iTunes, but only 136 show on my iPhone. I have the view set with iTunes Match on and "Show All Music" on.
Any suggestions for these?