There numerous bits of software out there that will convert a DVD into either an MP4, AVI or MKV file. It's really all down to personal preference.
Myself I'm a bit old school as I've been ripping and watching on a "small device" since my HP iPaq using a combination of DVD Decrypter and AutoGK both completely free.
This article lists a number of DVD video converter software. Some free, some pretending to be free and some that charge. You'll probably find you'll have to experiment a few times.
As for software on your phone to watch with my preference is MoboPlayer this seems to handle most formats without complaint.