You have to tell iTunes to Sync with a new (to you) iPod.
Connect the iPod to your computer and select the iPod's icon once iTunes shows the icon at the top, just below the menu bar:

That shows you the Device/Settings/Summary pane.
- Click on the Device/Settings/Music pane (1.):

- click on the Sync Music box (2.) to add the tick (check mark)
- click on the Entire music library radio button (3.). Note that section 4 will not be displayed
- click on the Sync (or Apply) button in the lower right corner of the iTunes window (not shown in the screenshot). At this point, if the iPod has been synchronised with a different iTunes Library, you will see warning that the existing media on the iPod will be deleted and replaced by the content of your iTunes Library
If these steps do not resolve the issue, please let us know which step failed to work as expected and mention what did happen.