If you're upgrading from, Windows 8 Pro, Windows RT, Windows 8.1 Preview, Windows 8.1 Pro Preview or Windows RT 8.1 Preview, the process is basically the same: You launch the Upgrade installer from Windows Store, run the installer while the PC or device is offline, reboot a few times, and then emerge with the OS upgraded. Here's a visual guide to this process.
Note: The only major difference between these installs, aside from the installer download size, is that those with Windows 8.1 or RT 8.1 Preview will need to reinstall all of their Metro-style apps and desktop applications when the upgrade is complete.
For a complete rundown of what upgrade options are available to each Windows version, please refer to my post Windows 8.1 Upgrade Guide: Electronic Upgrade Options.
OK, let's dive in.
Windows Store. You will see an Upgrade Windows tile.
Windows 8.1/Windows 8.1 Pro/Windows RT 8.1. This landing page will help you trigger the downloading of the Windows 8.1 installer.
Installer downloads. Oddly, you don't see this screen, or any download progress, with Windows RT.
App reinstall warning. If you were using a Preview version of Windows 8.1 or Windows RT 8.1, you'll be warned that you will need to reinstall your apps after the upgrade is complete.
Restart required. Tap Restart Now to begin the upgrade. Otherwise, it will happen automatically after a timer expires.
Installation. Your PC will reboot and begin the install process.
Installation continues. Your PC could reboot 2-3 times in total as install completes.
Out of box experience. Once Windows 8.1 has installed, the PC will reboot and you will need to step through an out of box wizard in which you will agree to the license terms, choose between Express settings and a more manual configuration, sign in to your Microsoft account, and agree to use SkyDrive.
App installs. Once that process is complete, Windows 8.1 will install its default app set and links to your previously-installed Metro-style apps so you can manually install them afterwards.
Done. When everything is complete, you will be presented with the improved Windows 8.1 Start screen.