The iPod Classic has no Wifi, so no internet connection, and as such no way to update form within itself.
To update the software on an iPod classic you must connect the iPod to a computer running iTunes.
From the iPod Classic Manual:
Updating and restoring iPod software
You can use iTunes to update or restore iPod software.
It’s recommended that you update iPod classic to use the latest software. You can also restore the software, which puts iPod classic back to its original state.
•If you choose to update, the software is updated, but your settings and songs aren’t affected.
• If you choose to restore, all data is erased from iPod classic, including songs, videos, files, contacts, photos, calendar information, and any other data. All iPod classic settings are restored to their original state.
Update or restore iPod classic:
1 Make sure you have an Internet connection and have installed the latest version of iTunes from http://www.apple.com
2 Connect iPod classic to your computer.
3 In iTunes, select iPod classic in the device list and click Summary. The Version section tells you whether iPod classic is up to date or needs a newer version of the software.
4 Click Update to install the latest version of the software.
5 If necessary, click Restore to restore iPod classic to its original settings (this erases all data from iPod classic). Follow the onscreen instructions to complete the restore process.
https://www.apple.com/support/ipodclassic/