We recently faced a similar problem. To extract the clip from a (non-copyright-protected) DVD, I had good luck on a Windows machine using VLC video player, which is free and widely available. Here's how:

http://www.howtogeek.com/howto/2686/how-to-copy-a-dvd-with-vlc-1.0/

If you have a Mac, there is a tutorial on how to extract and burn a DVD clip here:
http://tvcrit3.tvcrit.com/content/view/68/116/
There is one small gotcha about the free program MPEG Streamclip and DVDs: to work properly, it requires a $19.99 software component available from Apple: the QuickTime MPEG-2 Playback Component:

Mac version: http://store.apple.com/us/product/D2187Z/A
Windows version: http://store.apple.com/us/product/D2189Z/A

Ultimately, however, I should confess that rather than fiddle around with all this, and because I wanted to play the clip on a wall-mounted DVD/TV player in the exhibit rather than as a digital file, I wound up paying a modest fee (our budget was small, too) to a local video-conversion company to have the clip extracted and burned to a DVD: http://www.filmtransfer.com/

Patrick Leary
Wilmette Historical Museum
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