im confused on how apple music works

I am going to assume you are talking about Music app on iPhone and not iTunes. I am also assuming that you are paying the monthly subscription to Apple Music. First you need to go to Settings>Music and turn on Show Apple Music and iCloud Music Library. When you click the + sign you are adding the song to your library, which no, you don't pay a separate fee, and yes you can add them to playlists. But at this point you can only listen to the song by streaming it (must be connected to internet through wifi or cell service). If you click the cloud icon, the song gets downloaded to your iPhone. Now you can listen to the song without internet connection. This does not take up space on your iCloud (but does take up space on your iPhone). When you stop paying for Apple Music monthly fee, you no longer have access to these songs.