Find the track or album you wish to delete and simply swipe it to the left, you'll see a red box with Delete appear. Tap this and the album or track will be removed.
Note that if you don't have the music backed up in iTunes on your Mac, or in the cloud, you might lose the album or have to re-import it to iTunes if you want to add it to your phone again. If you bought the music from iTunes you will be able to download it again for free.
And remember to return to Settings and turn back on the Show All Music option so you'll be able to download the albums you've bought from iTunes again.
How to delete music from an iPhone: All at once
If you have a lot of albums stored on your phone, or just want to wipe the slate clean and start again, then there is a quick way to delete everything in one go. To do this navigate to Settings > General > Usage then in the Storage section you'll see the option to Manage Storage. Tap this.
You'll next be presented with a list of all the apps on your phone that are currently storing data.
Scroll until you find the Music app, then tap it to continue.
Your music library will be displayed, with the space each album takes up shown to the right of its title. In the upper right hand corner of the screen there is an Edit button, tap this and red circles will appear by your content.
To delete everything just tap the one next to All Songs.
Alternatively, if you've seen something you'd like to keep, then you can just tap the circles by the albums you want to remove. Once you've made your choices go back up to the top right corner and tap Done.
How to delete music from an iPhone: Using iTunes 12
Another tried and tested solution, for those who don't mind plugging their iPhone into a computer, is to use iTunes.
After connecting your device click on the iPhone icon in the top left area of the screen, then select Music from the On My Device section in the left-hand column.
In the central pane you'll see the various artists, albums, and playlists stored on your phone. To delete them first use the cmd+A key combination to select everything, then hit the backspace/delete key.
You'll be asked if you really want to delete the chosen music from your device, click on Delete and said items will promptly disappear.
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