Installing Windows 8 from a USB drive or DVD without upgrading from a previous version of Windows (e.g. 7, Vista, XP):
Go to the following page and select "Windows 8" to download WindowsSetupBox
http://windows.microsoft.com/en-us/windows-8/upgrade-product-key-only
Run WindowsSetupBox.exe
Enter Windows 8 product key purchased from Microsoft
Select "Install Windows"
Select "Install by creating media" after the "Downloading" progress bar completes
From here, you have a choice to download an .iso or directly create a bootable USB drive installer.
Some things worth noting:
A Windows 8 product key is not a Windows 8.1 product key:
A Windows 8 product key will not work with a Windows 8.1 installation. However, once Windows 8 is installed, you can upgrade for free to 8.1 through the Windows Store app.
Download the ISO as a backup:
If you download the .iso, then you can always create a bootable USB drive yourself later or burn it to a DVD. Having a backup up of the .iso can be handy.
Making a bootable USB installer without the WindowsSetupBox:
I have had good results using Your Universal Multiboot Installer (YUMI) to create bootable USB drive installers for both Windows and Linux distributions:
http://www.pendrivelinux.com/yumi-multiboot-usb-creator/
Edit: when you paid to upgrade from a previous version of Windows, you should have received an email with your product key for the version of Windows you upgraded to.