This is a topic that has been covered in-depth on this forum.
You can delete individual songs by swiping across them and tapping the delete button. Or, in the Artist of Album view tap-n-hold for a second, then tap the "x" in the upper left to delete. Or you can delete all downloaded music by going to Settings > General > Usage, tapping Music, then swiping and tapping the delete button.
This will not remove the music from the cloud or the iTunes library.