How can I remove my apple ID

Navigate through Settings--->iTunes & App Stores and tap on your Apple ID. A Pop up will appear in which
you will have the option to view Apple ID, Sign out and iForgot 🙂

Sorry but this does not seem to work if it's an Apple ID owned by the previous owner of the computer so that it is not possible to sign into the account.

Why do you still have data and content on a computer or iDevice from a previous owner?

Restore the device as new.