I am currently running an evaluation of Windows 8, as can be seen by the following screenshot of the bottom right hand side of my screen.
How can I upgrade to the full, non-evaluation version of Windows 8?
I believe you can't, the version you're running will be valid only until the trial period finishes without the possibility to upgrade to a full version.
Actually, from the Windows 8 evaluation website, at the "Things to Know Before You Start" section:
Follow these simple steps to upgrade to enterprise:
Enterprise installation media x86 or x64
Q: Will this keep my metro apps too?.
Q: Hmm windows border color is white?.
Q: Why is the System32\wlms\wlms.exe still present in enterprise?.
Q: Can Enterprise Eval be downgraded to Core or Pro.
Q: Is this officially supported by Microsoft
You will need to purchase a valid license key for Windows 8 Enterprise and enter it though the activation wizard found in the control panel.
If you want a different version such as Home or Pro, you will need to reinstall Windows 8 with the proper version, which will then accept the proper key. This is because Windows recognizes Enterprise as an "Upgrade" over home or pro and it will not let you enter an "inferior product key".