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Automatic updates mean two things:

• a scheduled job (via the /etc/cron.daily/apt script) to automatically update the package list, upgrade packages, etc.
• notifications to the user about available updates

To turn off the scheduled stuff, start Ubuntu Software Center (it's in the Applications menu). Go into Edit / Software Sources / Updates and clear the "Check for updates" checkbox. To achieve the same via the console, change all values (matching the pattern "APT::Periodic::*") to "0" in /etc/apt/apt.conf.d/10periodic config file.

To turn off notifications for the current user, go into System / Preferences / Startup Applications and either clear the checkbox of the item "Update Notifier" or remove it alltogether. To achieve the same via the console, you've several options:

• To disable for the current user, copy the /etc/xdg/autostart/update-notifier.desktop file into $HOME/.config/autostart and add a new line with a X-GNOME-Autostart-enabled=false content.
• To disable for all users, you can either uninstall the update-notifier package ...
• ... or you can edit the /etc/xdg/autostart/update-notifier.desktop file and add the same new line as specified in the disabling for the current user section.