The software tools
Handbrake is a free open-source front-end to libavcodec, the leading audio/video codec library. Libavcodec, in turn is part of the FFmpeg project, a complete, cross-platform solution to record, convert and stream audio and video. FFmpeg is a tool best used by video-professionals. Handbrake, which is available for Linux, Mac, and Windows, gives you access to some of FFmpeg's power but it's much more suited for use by people who just want to easily and quickly convert their videos into formats they can watch on their TVs.
Specifically, Handbrake can import most video formats and transform them into the MP4 and MKV (Matroska video format) containers. Most, but not all media servers and extenders support MP4. Fewer still support MKV.
Handbrake does not, however, include software to decrypt the video and audio on a DVD into a format it can then translate into a format you can stream. For that you'll need another program, such as DVD43, DVD Decrypter, and MakeMKV. The last program, MakeMKV, which is shareware, is the only program I trust to decrypt Blu-Ray disks.