You don't... Since all of your songs are in your iTunes library, you set up syncing for the new iPod from that same iTunes library. iTunes treats each iPod separately, even if you connect both at the same time. If you want the same songs, sync the same songs. If you want different (or more songs), sync those songs.
A convenient way to set it up is to create one or more playlists in your iTunes library, with songs for your iPod (or you can use existing playlists). Then, select the iPod in iTunes so that you see its Summary settings screen. If it's the latest iTunes 12, on the iPod's screen, in the sidebar, under Settings, click Music. Over to the right, check the box for Sync Music. This enables automatic syncing. Below that, choose the option to sync Selected playlists, artists, albums, and genres. Below that, under Playlists, find the playlist or playlists with the songs you want on the iPod, and select (checkmark) them. Click Apply.
iTunes syncs the songs (and playlists) in your selection to the iPod. Going forward, to update songs on the iPod, just update those playlists in your iTunes library. The iPod does not need to be connected. Then next time you connect the iPod (or click Sync if already connected), iTunes automatically updates the iPod with the same changes.