I use it sometimes but am unsure of how to play it in the background while I game. Do I simply play the music I want through Spotify and then load up the game?
You can start playing music before you launch the game, and it will just continue in game. Or you can launch the game first, and then start it at any time when you're already playing: just hold down the PlayStation button on the controller to bring up the Quick Menu, and the Music side menu lets you control Spotify.
You can use any of the recommended playlists, or make your own playlists. If you are going to make your own playlists, I recommend doing that from a Mac/PC, it's just way faster and easier than on other devices. The beauty of Spotify is that it's available on Mac/PC/iOS/Android/PlayStation, so you can make playlists and have them available pretty much anywhere.
In terms of the in-game music controls, you can use the Quick Menu "Music" sub menu to do all of that stuff: play, pause, skip forward/backward through tracks, set shuffle, repeat, adjust Spotify volume (independent of game volume).
Once we got the ability to customise the Quick Menu, the first thing I did was put the Music item at the top