Apple's made Apple Music front and centre of the new iOS 8.4 Music app, which means it's annoying if you don't want to use it. Thankfully, it's pretty easy to switch off.
If you're not interested in Apple Music, or simply annoyed given it also makes accessing your own playlists a two-tap process, head to Settings>Music.
Right at the top is a toggle switch to "Show" Apple Music. By default under iOS 8.4, this will be toggled to the green "on" position. Switching it to off removes the "For You" and "New" sections in the music app, and brings the playlists toggle back to the bottom of the screen.
It's still possible to access Playlists (via My Music>Playlists) in iOS 8.4 if you are using Apple Music, but this makes it simpler if you've no interest in the Apple Music service.