Welcome to Android Central! True sync solutions are hard to come by (i.e., syncing meaning that whatever changes you make on the computer are made on the phone as well whenever you connect).
doubleTwist and
iSyncr are commonly mentioned, but I also see some complaints about imperfect syncing.
The easiest thing to do is to upload your entire music library to your Google Play Music library in the cloud, using Google Music Manager:
https://support.google.com/googlepla.../1229970?hl=en. This makes all of your music available online on any device, which you can stream or download locally.
Another solution is simply to copy the music files to the phone's Internal Storage or microSD card via USB connection. This isn't a true sync, though--so if you make changes to your music library on the computer, it won't be automatically reflected in the phone's library.
