The "intended" method to shutdown in windows 8 is to open the Charms side bar first, then choose settings, and then choose "start/turn off" (don't know exactly what it says in English, my OS is in Spanish).
To open the charms bar you have several options:
- the easiest one, just press WindowsKey + C
- move your mouse cursor to a corner on the right side of the screen, then move the mouse down (f upper corner) or up (if down corner), that shows the charms bar.
- if you have a touchscreen, slide your finger from right to left across the right edge of the screen.
- if you are using a touchpad and it supports it, you can also slide from right to left in the touchpad (from outside the touchpad towards it) to open the bar.
Another way to shutdown, is to press Alt-F4 while being n the desktop. that brings up a menu where you can choose to shutdown, restart, log off, hibernate... etc
If you are in any other app, you can quickly get to the desktop by pressing Windows + D.
So, the fastest way to shutdown would be:
Windows + D (if not on desktop already), Alt+F4, then S* to bring but the "Shutdown" option if it's not already selected, then Enter, and there you go.
*Again, I don't know exactly the name it shows in English, in Spanish it says "Apagar", so I only need to press the A key and then enter.