First I tried to install SQL Server 2012 RC0 as I had the installer already, but I ran into an issue (missing system CLR types). I decided not to handle this, since SQL Server 2012 RTM is available now. So I tried to install that one instead.
A smaller issue came up again. But Andre Ziegler saved my day with his post in one of the Windows 8 Developer Preview forums.
So, it's better running the script before you start the installation.
You'll have to run cmd as administrator, insert your Windows install disc and type:
dism.exe /online /enable-feature /featurename:NetFX3 /Source:d:\sources\sxs /LimitAccessDon't forget to check the drive letter of the source and replace it if necessary.
SQL Server 2012 is installed and running now on Windows 8. Thanks Andre :)