When I changed over to Google Music, I transferred all of my music from all of my devices, phones, multiple pcs etc, all on to the one pc that I had my iTunes on. Apparently I had multiple versions of the same songs all over the place, and I got to spend some time removing duplicate songs, kinda cleaned it up some... Lol
Then installed Google Music, and the pc program searched the entire pc... Uploaded everything to Google Music. Then I installed the app on my phone. I also use Chrome on all of my pcs, laptops etc, and can listen to my Google Music directly through there, and not always from my phone while working or traveling.
Biggest thing to remember is that if the song file is only on the pc, you have to have a data connection to listen to it on the phone... Or in the app you can select to download it to the phone but (limited to a few downloads per song). Therefore, whenever I go on a trip, I usually will transfer a song list directly to my phone from the pc, or rely on a data connection.