DVDs use the VOB container format for storing video, audio and subtitles. If Final Cut can’t import those directly, you can use a transcoding tool to convert to something more universal like MP4. I like ffmpeg for this.
Something like this should do it: ffmpeg -i <input-file>.vob -acodec copy -vcodec copy <output-file>.mp4
The “copy” options tell ffmpeg to put the audio and video streams into the new container (MP4) without re-encoding. Anytime you re-encode you’ll lose a bit of quality.
Alternatively, you can get it using Macports or Fink.
Update: Final Cut Pro might not support AC3 audio in an MP4 container. It might be better to re-encode the audio to the more common AAC like so: ffmpeg -i <input-file>.vob -acodec libfaac -ab 384k -vcodec copy <output-file>.mp4
Finally, I’ve heard there’s a trick where you can simply change the extension from .vob to .mpg, which might help programs that don’t recognize VOB. This works because VOB is just a specific type of MPEG.
If you end up re-encoding the video you might as well choose a codec that works really well for editing. Codecs designed for playback such as MPEG don’t store every frame of video which can make for inaccurate/sluggish timeline scrolling. DV is a good choice since you’re working with standard definition. M-JPEG is very similar to DV and works at any resolution. If M-JPEG isn’t available, you can use a codec such as MPEG-2 or MPEG-4 if you set the GOP (group of pictures) size to 1. This forces MPEG based codecs to store every frame, increasing the size, but making editing easier.