Very easy to do, you just need to install two free programs:
1) DVD43: http://www.dvd43.com
(Reboot after installing)
3) Insert DVD, cancel any auto-play
4) Run Handbrake, under Source, browse to the VIDEO_TS folder on your DVD drive
5) Under Destination, browse to any folder on your PC where the converted video will be stored, pick an appropriate name for the movie.
6) Under Presets, click on iPhone/iPod Touch, do not adjust any other settings.
7) Click Start, and wait 30 minutes to 2+ hours (depending on computer speed, and DVD length)
8) Drag the converted (.mp4 or .mpv) video file into Movies in your iTunes library
9) On the iPhone in iTunes, click the “Video” tab, then select the Movies you want to sync.
10) Sync, done. Movie will show up on your iPhone’s iPod “Videos”.
Tip: When playing, double tap to adjust the zoom in letterboxed movies.