First, one takes a DVD ripper. For example, DVD Decrypter for Windows or QuickRip for Linux. In a familiar operating environment, setup should not take long.
Then one rips the files, in the process removing copy protection measures (for example CSS/CPM). This process may take quite a while.
Then, if something awful should happen to original disks, one can create replacement disks (must split or recode -- current burners cannot do double layer) or watch the movie from hard disk.
On the issue of playback from hard disk, I will try providing better descriptions -- after making a couple of experiments.
So far, I have not needed my backups. However, given the physical imperfection of all data storage... this time will come.