[SERIOUS] Friend's father passed away yesterday, what can I do to support them?

So today after school I ran into one of my friends (I'd been meaning to talk to them, but I was caught up with the new semester). Let's call him "Jeff". Jeff is one of the happiest, nicest people I know, so I'm shocked to see him looking this sad. After a brief conversation, I found out that his father passed away due to unknown medical reasons, and that he hasn't told anybody else about this. I talked to him for a bit and it seems like nobody's there to help him through this (and definitely not the guidance office, who interrogated him with questions like "did you resent your father or harbor negative emotions against him?"). What can I do to help him without being that guy saying "I'm sorry for your loss" over and over again? I'm a bit of a social klutz, so any help would be greatly appreciated.