It is a violation of American copyright law to copy copy-protected DVD movies.
Having said that, you must use an application to break the copy protection scheme of the DVD movie, rip the DVD movie files from the DVD to your hard drive, and then you can burn a copy of the movie files to a blank DVD disk.
The advice I just gave you paraphrases the advice of commercial copying software like Roxio Easy DVD/CD Creator and Nero Burning. Don't believe me? Get a copy of one of these applications, and search their help files.
DVDShrink appears to be the most popular and most useful of the ripping and burning free applications available. DVDShrink not only will rip the DVD movie files, it will also compress the files to sizes small enough for one DVD disk. This compression is necessary because the files on most DVD movies can fill two blank DVD disks of 4.3 GB disks. When used on a computer where Nero Burning coexists, DVDShrink will also burn the files to a blank disk.
As far as I know, no one has ever been prosecuted for using DVDShrink to do what you want to do: i.e. for backing up your own DVD movies.