When you buy a DVD from the store, you are not buying the license to decode the contents of the DVD. The ability to decode the contents of purchased and encrypted DVDs is embedded in DVD players, and privately licensed to operating system vendors.
On Linux, you can obtain a license (bundled inside of a DVD player application) by purchasing OnePlay DVD Player. This is the legal, software-based player for encrypted DVDs on Linux.
As Fluendo is a sponsor of the popular and very effective GStreamer technology, the purchase ($18 US) is a bargain. Even if you do not choose to use it, you'll invariably be using GStreamer, so if you feel inclined to support the company then purchasing a OnePlayer license, while somewhat unrelated to the free multimedia framework, is a good way of doing so.
If you live in a region that does not respect the laws created by the MPAA, or you believe that DVDs should be inherently playable and reject your local regional laws forbidding you to decrypt content on DVDs, you can use the reverse-engineered decryption library libdvdcss (unrelated to the Internet CSS technology).