Well, when this happens you could do ctrl-shift-f2 and get into a shell and see if you could work out what is missing. But for me the easiest way was to boot into a live usb, this way you are able to access the file system where your installation is and the just transfer the files.

I did get a error message when I edited the kernel boot (press e in GRUB) and was able to see which file did cause the first hiccup. But it could be dozens of files corrupted.

The files was: /usr/lib64/libgdk_pixbuf-2.0.so.0 and the error message was that it was to short.

After knowing that and with a internet connection (I run on a 3g dongle, couldn't get it connect via terminal) I could reinstall the pixbuf packages and hope that that was the only file corrupted (not likely from what I got).

As for a correct way, I don't know. One thing in windows that is good (and I don't know if there is this functionality in linux) is that you can just restore the system to a earlier state. The one thing I think linux is lacking, if it doesn't exist.

Sometimes there's nothing you can do. Most of the time you can try the magic SysRq key combos to sync/unmount and reboot. Wikipedia has a nice article on it.