How do you get music that you have already purchased into the new apple music?
Open iTunes, then (if on mac) click the word iTunes in the menu bar and turn on "iCloud Music Library" this will sync all music and playlists to your iCloud, and will be matched with content found on iTunes. 

If on Windows, open iTunes. Then in the File menu, click preferences, and turn on iCloud Music Library. 

After this, you will need to open settings on all of your other iOS devices, and turn on iCloud Music Library. 

Please note that if you choose to download music from the Apple Music service it is DRMed and will not be editable as your iTunes purchases are.