In order for you to edit your videos stored on the video DVD, you need to rip it via
MacTheRipper/RipIt/Fairmount, if the video DVD is copy protected (all commercial video DVDs are). If it is not copy protected, you might be just able to copy the Video_TS folder onto your HDD. Now there are two ways to convert the MPEG-2 compressed footage.
1. Get
Handbrake and convert the footage to an .mp4/.m4v file with the H264 codec.
Further reading on Handbrake on transcodding video for iMovie.
Then use
MPEG Streamclip to convert/export the .avi or .mp4/.m4v file to a QuickTime (.mov - CMD+E) file encoded with the DV codec or the Apple Intermediate Codec (AIC) or to a DV file (CMD+OPTION/ALT+E). Both, .mov and .dv, can be read by iMovie.
2. Get the
QuickTime MPEG-2 Playback Component from the Apple Online Store for 20USD, open MPEG Streamclip, in there go to File > Open DVD and select your Video_TS folder on your HDD. Then either export it as QuickTime with the DV codec or AIC or as DV file as explained in step 1. This saves you one encoding process, therefore time and image quality loss.
Screenshots:
MPEG Streamclip export options
Handbrake export as .mp4 - example