How do I change the iPod Touch Apple ID if I purchased it off someone else

The seller needs to give you the password to unlock that iPod. That's the activation lock and it cannot be user defeated (it was meant to be an anti-theft program to keep thieves from wiping and reselling stolen devices....not accusing or anything just saying)

If the person cannot give you the password to remove the Apple ID and get that device off the original owner's iCloud account then get your money back.

If a 4G or older iPod:

Place the iOS device in Recovery Mode
https://support.apple.com/en-us/HT201263
and then connect to your computer and restore via iTunes. The iPod will be erased.
If you forgot the passcode for your iPhone, iPad, or iPod touch, or your device is disabled
https://support.apple.com/en-us/HT204306
If recovery mode does not work try DFU mode.
How to put iPod touch / iPhone into DFU mode « Karthik's scribblings
https://geekindisguise.wordpress.com/2009/07/16/how-to-put-ipod-touch-iphone-int o-dfu-mode/

For how to restore:
Use iTunes to restore your iPhone, iPad, or iPod to factory settings
https://support.apple.com/en-us/HT201252

If the iPod is a 5G or later one then the previous owner has to do this:

Turn off Find My iPhone Activation Lock - Apple Support

Then do the actions for an older iPod above

If you can't get the previous owner to turn off the Activation lock then return for a refund. If you can't do either then turn into the police since it is worthless to your and is likely lost or stolen. Apple will not help