You have 2 choices.
1- sync with iTunes. Make sure sync favorites is checked off.
2- activate iCloud on your phone and install the iCloud software on your computer. No syncing is required. If you add a favorite on your iPhone or your computer it's is automatically synced to the other device.
The common method is iTunes, and you can use it to sync with your iPhone. To do so: Connect your iPhone with the computer > Open iTunes on your computer > Drag and drop your favorite music from your computer folder to iTunes Library > Click iPhone icon on iTune > Music > Select Entire music library > Click Sync button to make it.