How can I get my serial number for my ipod touch?

If it was registered to your support profile then you can get it from that : https://supportprofile.apple.com/

Or if you have a backup of it on your computer's iTunes then you can go into Edit > Preferences (iTunes > Preferences on a Mac) and on the Devices tab hover your mouse pointer over its backup name

If you have the original packaging or receipt, it should be on there as well.

Also, depress the Control key and the click on About iTunes