The subject says dvr, but your question asks about dvds. I'm assuming you're backing up dvd movies. If so check this site out:
http://www.afterdawn.com/guides/
The software you probably need to use is dvdshrink because most movies on dvd are on dual layer which cost a fortune. That will let you compress the content on a dual layer disc to fit on a regular 4.5MB disc. Copying copyrighted material is illegal, but if you are just backing up discs, that program also works a decrypter for copyright protected movies.
There is other software on that site, but dvdshrink is free. They also have a simple walkthrough for using the software.