We have "The Tenth Good Thing About Barney," too.

We've had pets die in our family, and I had an early miscarriage, and each time ds' questions were different (he's 5 now). At first, when he was 2, his only questions were along the lines of "Will Piper come back?" and my answers were just gentle explanations that death is final. Now his questioning is more about survivors: "When you die, I'll be sad." I affirm that when someone we love dies, it's very sad and we miss them.
I explained that when someone dies, their body is done ... "empty". I let him see & touch the pets' dead bodies (he wanted to). Obviously this wouldn't be practical in every situation, but he was able to experience how they weren't warm anymore, how they didn't respond, etc.
I'm not religious, but I do believe in some kind of afterlife/rebirth, so I've explained to ds that some people believe there's an important part to us that we can't see, a special part that makes us who we are, and that after the body is dead & empty, that special part still exists but we can't see it. I told him I didn't know where it is. This only came after he had a firm grasp on the permanence of physical death, of course.
We also talk about how even though dead people are gone & don't come back, we always have our good memories of them, in our hearts and minds, and nothing can ever take that away.