This is what he says about apologies:
"Proper apologies have three parts:
1) What I did was wrong.
2) I feel badly that I hurt you.
3) How do I make this better?"
Source: Randy Pausch, Jeffrey Zaslow, The Last Lecture, 2008, page 162.
Randy died on July 25, 2008 at the age of 47 from complications from pancreatic cancer.