Allan - thank you for the answer. I will find out about the disks, but an alternative was suggested to me. This is to create a new user with Admin privilidges, and then delete the original one. This will delete all his data (except for any shared files that I could remove separately) This seems pretty simple - will it do what I want - have a working system with the data removed?
Yes, that would work but I would use the "Secure Empty Trash" option in the Finder menu when you finish moving stuff. Make sure the computer works from the new account first.
The advantage to teh new user option is that, if the OS has been upgraded, it stays at the later level. If you find the disk and the computer is going for reuse as opposed to recycling, pleas give the new owner the disks. They have important utilities for troubleshooting.
Secure Empty Trash is more secure than a regular delete, and will probably be enough to prevent a lower-level criminal from finding anything useful. You can also use Disk Utility's "Erase Free Space" option after secure empty space to give a second wipe.