My mother-in-law passed away when my youngest son was 3 weeks old and my oldest was 2 and a half. I did a lot of reading (which took a lot of digging) as to how to best explain to my son what happened to Nana. Death is something that we in North America don't handle very well. We know we have to deal with it at some point in our lives, but we really don't want to. We don't want to think about it, because thinking about it often makes it too real.
Of course with death being such a final, yet foreign concept to us, explaining it to a child can be difficult. We really need to be careful with the language that we use to our kids. For example, many of us will use the words: 'putting the dog to sleep' when we put down our dogs. We, as adults get that. For a kid that could be very traumatic. Kids are so literal. Sleeping is sleeping and here we have just told them the dog is sleeping. But they know that the dog never came back. Well, what does that tell our kids about actual sleeping? Or telling our child that we 'lost' Aunt Sylvia. "When will we find her?"
Some people (myself included) have religious views on heaven and afterlife. Personally, I take the thought of my mother in law being in heaven as a comfort. Some people will tell a child that God loved so and so so much that they wanted them with them in heaven. That's not how I explained it to my son. I didn't want him to develop a fear of God taking those that he loved away from him, or, being afraid that God would take him away from us.
I think the best approach you can take is to just be direct and use the real words. Very simply, "Nana died". They make take this with a shrug and go off and do their kid thing. They may have questions. Either reaction is valid. Remember kids often don't 'get' death. They aren't being indifferent on purpose. They aren't being gruesome with their questions. They are just being kids. You may have to tell them more than once as things come up. Your child may ask you why you are crying. Tell them the truth. "Mommy is sad because Nana died". They really don't need to know more than that.
"Why" is often a question that they will ask. They don't need any unneccessary details. You don't need to go into great details about cancer or car crashes or whatever it was that caused the death. You may wish to say that so and so was very sick and their body stopped working. Tell them what they need to know in words that are kid appropriate.
You also may need to tell them many times. Kids forget and they don't understand it. Don't take it personally. I know that you are going through the grief process yourself (which is never easy) and the last thing you want to hear is, "Can we visit so and so"? Again, you just have to be gentle and firm. "We can't honey, because so and so died which means that we can't see them any more" (If you do have a belief in heaven this is also a good oppourtunity to add: "one day, we will see them in heaven, but until then we can remember them in pictures and stories").
Kids will also be affected by many different kinds of deaths: the death of a pet (no matter how small) could hurt them just as greatly as the death of an aunt. They can also be affected by deaths that they see in the media and in movies. Kids hear the news that we listen to. They may ask about a little girl in their city who was killed. They may be genuinely upset at Mufassa's death in the Lion King. Emotions are honest reactions and it is healthy for kids to express these feelings, without us brushing them aside. (How many of us cried at Beth's death in Little Women? - an honest emotional reaction to a book)
You may need to be prepared to talk about whatever death your child has encountered for years afterwards. This is normal and healthy too. We all still think about people (and pets) that we have loved and lossed. We have memories that we need to hold on to, so do our kids. So if my son has a need to talk about Nana (or 'my Nana who died' as he puts it) then great (even if it is sometimes hard for us). We need to take the time to remember her and the life that she lived. So does he.
Whether or not your child is small (as mine was) or a little bit older when they have a death to deal with, we need to help them deal with it. I know my sister-in-law faced these same questions with her then 14 year old and took a very similar approach. Open, honest with terminology that was appropriate.
Whether you are reading this because of something you are going through now, or tucking away this advice for use at a later time I hope you find it helpful. I empathise with you because it isn't easy, but you will get through it and so will your kids.