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Here's how to delete a song on your iPhone, from the iPhone user guide:
Remove a song from iPhone. Tap Songs, swipe the song, then tap Delete. The song is deleted from iPhone, but not from your iTunes library on your Mac or PC, or from iCloud.
YES - i need help with this too. I just unchecked "Sync Music" in iTunes under my Device Menu on my laptop, synced, and now my whole library still shows up on my phone with little clouds next to them prompting me to download. This is very annoying. I just want it all clean and clear.
This did not work for me. I see a cloud icon next to every song in the Music app. When I click the cloud icon, the song downloads. Then I can swipe and delete appears. But once I delete the song, the cloud icon reappears. I tried turnig off "Show all Music" in the itunes & App store prefs but now only half the songs appear and none respond to the swipe gesture (i.e. can't delete them). I want these songs completley off my phone and out of the music app. How do I do this?!?! this is insane!!!