I use the Socratic method combined with genuine curiosity. In this case, I'd probably start with a fairly open ended, "What happens when you die?" and go from there, question after question, all earnest, with a true desire to know and understand the other person, going as deep as possible. I've had discussions like this about God with strongly religious people, and they're very happy to try and explain; the fact that they have little real foundation dawns very slowly in such circumstances, leaving many avenues for exploring new ideas.

The main answer to avoid is, "God works in mysterious ways." Haven't found a way around that one yet.