Q: HOw do you delete songs from a device?

You should be able to delete them directly on the phone by swiping across a track name if you want to delete just a track, an album name on the album selection tab, or an artist on the artist tab. Or you can do it when connected to your computer's iTunes, either by changing your sync selection and re-syncing, oy by selecting the Music section under the iPhone 'device' on the left-hand sidebar of iTunes e.g.

And on the right-hand side of iTunes selecting and deleting that you no longer want on it