The Google Play Music service has always required the use of the Music Manager desktop program in order to upload your songs to the service. It also monitored folders for new songs to upload and allowed you to download your collection. Unfortunately, it didn't always perform consistently and it was only available for Macs and Windows PCs, but now there's a new solution.
Google Play Music for Chrome, a lab feature, lets you upload your songs and even monitor folders for updates. As reported by The Verge, the feature will eventually roll out to all users, but can be enabled manually from the labs section.
To enable Google Play Music for Chrome, click the gear icon in the upper-right corner and select Labs. Enable Google Play Music for Chrome, then click on "Save changes."
Once it's enabled, go to My Library and click on the orange "Add music" button to start the Google Play Music for Chrome setup.
After you've completed the setup, your music collection will begin uploading. The next time you need to upload songs, you'll only need to click on the "Add music" button from My Library.
While your music is uploading, you can also try out the new mini player by clicking on the pop-out arrow, located all the way on the right side of the player controls.