Is there a way to easily use music from Google Play Music as ringtones on my phone?
I've got a way to do this that is really simple and doesn't require needing to download to your computer every time. I recommend using the music manager from google play to upload your existing collection of music, first. Otherwise, any track you want to make into a ringtone will need to be purchased first.
From your phone using the chrome browser, navigate to music.Google.Com. Don't follow the prompt to download the app, instead hit your menu button in the browser and look for the option to "Request desktop site." The music store should load the way you see it when at your computer. Tap next to the name of the track you want, in order to get the three dot menu to come up. If you own it download it, otherwise buy it. Now when you go to find it it'll be in your download folder. This is really just for convenience so you don't have to use your computer at all.
download the song on another device
use makeownringtone.com to cut the ringtone and download it
move the ringtone to dropbox
open dropbox on your phone and export the ringtone Ringtones or Notifications folder
I really like the app Rings Extended. From their Play Store description:
Replaces the standard ringtone picker with a new one that makes it easy to select from installed music tracks & other sounds. Just go to Settings or an application's settings for a ringtone and you will be prompted to use Rings Extended.