The underlying problem is that the Windows Update self-update mechanism is not working.
In order to successfully install Service Pack 1 you need at least Windows Update version 7.6.7600.256. Windows Vista RTM ships with version 6.0.6000.16386, and this version will not self-update because the file
wuident.cab (as of the version digitally signed July 14, 2012) provided by Microsoft's Windows Update servers contains an explicit instruction that WU versions 6.0.6000 and 6.0.6001 should not self-update. It is not clear why.
There may be one or more missing files on Microsoft's servers, because error 0x80190194 means that a 404 (File Not Found) error was received from the web server. However, this error does not occur if you are using a WSUS server, but the client still won't self-update. It is therefore possible that error 0x80190194 is not directly related to the problem.
Microsoft Support advised me that the problem is being worked on and that a KB article will be released in due course. They did not give me an ETA. Addendum: two years and counting. I think it safe to assume that the problem is unlikely to resolved at this point!
There are two ways to work around this issue:
Download and install Windows Update version 7.6.7600.320 using the download links provided in Microsoft's Knowledge Base Article KB2887535. Although no download link is provided for Windows Vista, the Windows 7 version installed successfully when I tried it. (Note: this download was not available when I originally wrote this answer, and I have not tested it on a Windows Vista RTM system. If you have done so, please let me know. The third-party download I originally linked to is no longer available.)
Download and run the off-line version of Windows Vista Service Pack 1 (or the all languages version) from the Microsoft Download Center. This will take longer to download and install than using Windows Update, but is officially supported.
In either case, once Service Pack 1 is installed, Windows Update will offer some additional updates and then Service Pack 2. Service Pack 2 should install successfully.
Note: Microsoft provides free phone support for problems installing service packs. See Microsoft's support page for the contact number for your area. In some countries this may be a toll call.