There is currently no official way to do this.
iTunes cannot rip DVDs as it can CDs to play across your local network.
While there is software out there that can potentially rip DVD and convert to an AppleTV compatible format, this would potentially require circumventing encryption on DVDs on commercial DVDs - as such this could be technically illegal in your country and Apple's T&Cs for the forum therefore prevent discussions of methods of circumventing copy protection, even if for 'fair use' with DVDs you have purchased.
The next Mac OS X version supposedly has Airplay to send computer video to AppleTV but whether it will work on all machines or just new ones (in a similar way to features not always working on older iPhones etc) we do not know. Also we do not know if things like the DVD player app or certain website content will be precluded from Airplay if the copyright holder disables Airplay functionality in the website markup.
you're best off buying a cheap DVD player. There is software out there (AirParrot) that allows AirPlay mirroring and using the TV/Apple TV as a second monitor, but doing full mirroring with sound has a major lag... Once Mountain Lion is released, AirPlay mirroring will be available at the OS level, but that doesn't guarantee that DVD Player will be able to mirror...