You can output a song list by tapping on the share icon in the Menubar to open the Share Menu and then choose Print to open the Print Preview Screen. Tap on the Print Mode Button in the lower-left corner to toggle to song list mode. Once in that mode, tap on the wrench icon in the lower right corner to open the Print Options Menu. Tap on the Output Options. Here you can select the songs that you want to appear in your list as well as use the Extras section to choose which columns to output.
Once the preview looks as you like, you can either tap on the Print button to send to an AirPrint-compatible printer or tap on the Share Button. This will let you AirDrop the printable PDF file to another device, or choose another app to open the PDF into. You can also export or copy the document using the Actions row in the activity menu.