You iPod syncs via the iTunes application. You don't need to buy music from the iTunes store to use the iTunes application.
Open the iTunes application and import whatever titles you have. Once you see them in your iTunes library, connect your iPod.
You iPod should show in the iTunes application. Once it does, they synch'ing should start. If it doesn't, you can manually start a synch. There are also setting where you tell the iTunes app what you want to sync with your mobile device. You may want to check them to ensure that music is set to sync.
