I use Nero which came with my DVD burning drive as the actual burning software, but I usually make an "image" file for the original DVD movie using a ripping software like DVDDecrypter or DVDFab to read the movie and format the "image" file. DVDShrink works pretty well too for this purpose, but any of these will take some time to learn how to use for creating a DVD movie backup.
If the movie you are talking about is a home video, say from a digital camera or VHS tape, then you will need a DVD movie producing software. My favorite is CopyXtoDVD for collecting various AVI or MPEG videos, and then burning a DVD menued disc for TV viewing. The VHS or other video tape procedure is the most complicated method which would require video input to your computer and a video capturing program to create the MPEG video on your computer.
Good luck with your project.