How to open "System > Administrator" -menu?

There's no "System" menu in modern versions of Ubuntu.

Just open the Dash (using Ubuntu button on the Launcher or Win key on your keyboard) and start typing program's name that you want to launch.

Also, you can access settings, provided in the former "Administrator" menu by typing "System Settings" in Dash, or by clicking "power" or "power cog" button in the top-right corner on the panel and choosing "System Settings".