I don't know the best program.
Is your aim to keep the video in DVD format or re-encode to something like AVI?
Re-encoding involves a loss of quality that might not be acceptable - but you have to decide.
I would start by opening the DVD in DVD Shrink and Re-authoring it into separate videos.
Run DVD shrink and 'Open disc'.
Assuming it's only one Title that contains the collection, click 'Re-author' and drag Title 1 from the right to left pane.
Click the double arrow thingy and select a segment to separate out.
Click 'Backup' and save the segment to a new folder (in effect a new DVD).
Clear the left pane and re-drag Title 1 from right to left;repeat selection and backup.
Repeat until you have all the new selections.
Exit.
When you have all these mini-dvds, decide if you want to keep that format or convert to AVI and continue to the next step.
