Here's the Apple script that will get the track information from Spotify for the current track. Once you have this, you just need a way to print the result somewhere. I use the Text Expander app on the Mac to insert text snippets with simple keyboard shortcuts.

if application "Spotify" is running then
    tell application "Spotify"
        if (get player state) is playing then
            set appProperties to properties
            set currentTrack to current track
            set songName to (get name of currentTrack)
            set songArtist to (get artist of currentTrack)
            set returnString to "\"" & songName & "\"" & " by " & "\"" & songArtist & "\""
            return returnString
    end if
    return (get player state)
end tell
else
return “Spotify is not running”
end if

Add the Script to Text Expander

Then you just add that to TextExpander.

1. Set "Content" to "AppleScript", and paste the script above.
2. Assign a keyboard shortcut you would like. I used "song;" (with a semi-colon).
3. That's it. Now, when you type that combination anywhere on your Mac, it will replace that with the name of the song currently playing.