By default updates are set to install automatically in Windows 8 - but if you wish to change settings or manually run Windows Update you can access it via Control Panel or PC Settings - see here for instructions on accessing Control Panel and PC Settings
via Control Panel
From the Control Panel click System and Security
then click Windows Update
Here you will see if any updates are available, when updates were last installed and you can also click Change settings if you wish to change automatic update settings
via PC Settings
From PC Settings click Update and recovery
On this page you can then see a brief summary of your update settings, and you can click Check now to see if any new updates are available
Updates installing prompt
After Windows Update automatically downloads and installs updates you will often see the messages below when booting or restarting your computer - these are updates which could not be installed when Windows is running so are automatically installed during a shutdown or restart - as the message states do not switch off your computer, wait a short while and the update process will complete automatically
Updates for Windows Store Apps
If any of the applications you download from the Windows Store has updates available then these will be automatically installed for you
But if you wish to manually check for updates then access the Charms Bar by moving your mouse pointer to top or bottom right corner, click Settings > App updates (as shown below)
You will then see the following screen where you can click "Check for updates" - if any updates are available they will be shown and you can click to install them