Hi,
If your Movies were digitized on a data DVD, as opposed to an authored movie DVD, they will be uncompressed and displayed by file name just as if they were stored on a disk drive. With a data DVD, you would insert it into an optical drive that is plugged into your computer, click on the DVD to open it, and then you can simply Option-drag the listed movies to your desktop. If they are not in a format that is compatible with iMovie, you can convert them to Mp4/AAC with the free download, Handbrake. (More about Handbrake below.)
Alternatively, if your movies are digitized on an authored DVD, such as from iDVD or Roxio Toast, then they would be compressed and in MPEG-2 format. When you click on the DVD's icon on your desktop after inserting it into your optical drive, you will see a folder that contains a VIDEO_TS folder and an AUDIO_TS folder. Ignore the AUDIO_TS folder. Open the VIDEO_TS folder and you will see a list of files. Copy (copy, not move) to your desktop the files that have a VOB extension. Ignore the rest. (As Ian mentions in his earlier post, Handbrake also can open the DVD menu contents, and you can proceed as above.)
The VOB files contain your movie. Once you have copied them to your desktop, you can use the free download Handbrake to convert them to H.264, Mp4/AAC files that Handbrake will do by default. Then you can import the converted files into iMovie.
You can get Handbrake here:
https://handbrake.fr/
A simple way to do it is to open Handbrake and do a File/Open Source. Navigate to your DVD icon on your desktop and choose it as the source from the resulting screen. Then do File/Start Encoding. Wait a couple of minutes for the conversion to complete. Then save and import the converted clip into iMovie.
If you simply want to convert the entire contents of an authored DVD to one movie in Mp4 format, you would open Handbrake and do a File/Open Source and navigate to the DVD's icon on your desktop. Then do File/Start Encoding. The contents of the DVD disk will be converted to an Mp4/AAC movie. You can then import the movie into iMovie and split it into segments if you wish.
All of the movies converted with Handbrake can be edited in iMovie.
-- Rich