It's amazing that for something which as adults is such a concrete (and inevitable) concept as death is, that when you try to explain it to a young child you realize just how abstract it really is. We had to explain death to a barely 3 year old last year. I think really it's all about breaking it into age appropriate concepts and keeping it both simple and direct. While it's harder to explain at this age, the emotional significance of this will (thankfully) also not generally match that of an older child or adult. They are also excellent fact based learners, with no preconceived notions about what makes a topic uncomfortable for older people to talk about. So use this to your advantage. Generally, stick to the fundamental facts (NO confusing euphemisms like 'forever sleep' or 'going away') in familiar terms and add in a little bit of emotional coaching. I'd start with something like this:
Something very sad happened. __________ died.
We're not going to be able to see them ever again.
When somebody dies, that means their body completely stops working.
They don't eat, speak, or play anymore, and they don't feel any pain.
You also won't be going to their house on weekends anymore, because they will not be there.
From now on, you'll probably go to ____________ on weekends.
It's ok for you to feel sad and upset about all of this. It makes me feel that way too.
I love you, and will do my best to answer any questions you have.
They're likely to ask some surprisingly tough questions. No dodging them. This may occur right away, after they've had some time to think about it, or more likely both. Answer them to the best of your ability, as honestly and truthfully as possible. Remember your answers, because they will remember them too. They're going to be reconfirming this information with you (testing you on it) over, and over, and over again in the coming days and weeks...And then more times sporadically over the coming months. The answers they get need to be consistent. At this age, they mostly learn through repetition, so it will be the exact same (word-for-word) conversation 100+ times. Communicating and discussing the questions, and answers, with the child's mother will be very beneficial to the child. The answers don't also have to be word-for-word the same between each of you, just consistent with each other. Some questions may require discussing how to answer it between you and the child's mother before providing fully answering the child.
Slowly the questions will stop, and be replaced by them reciting the entire series of answers you had previously provided to them, seemingly at random (and often inopportune) times. This will probably start off with reciting it to people they know and are comfortable with, and will eventually extend to being something they might bring up as a point of conversation with anybody they might talk to...Including friendly strangers, like the check out clerk at the grocery store. So be prepared for the whole world to know whatever answers you gave them...No pressure.
At first, start preparing to answer simple (LOL!) 'why' questions for each part of each statement above. It's ok to admit if you don't know, but maybe also try to reassure them you'll help get them an answer. Be warned though, one might think that as the repetition of the same information, followed by the same questions and same answers is rehashed enough times to start sinking in, that their minds will be put at ease. They will not. Their increased understanding and awareness will likely lead to new, more awkward, more uncomfortable, and more unexpectedly deep questions. You also may get some unexpectedly profound statements from them on occasion here too. Pay attention, as you just might learn some new things about your child as well.
At some point, showing and explaining to them some of the more common 'death' all around us in nature might also help. One that is particularly visible this time of year, is that of flowers. They can witness the whole life cycle of the flower within a few weeks time.
Regardless of the beliefs you're choosing to raise your child with, I would also urge caution introducing them to any new religious concepts that they're not already comfortable with. At least, not early on in this process. Otherwise it's largely just compounding the number of abstract concepts that the child is trying to wrap their mind around.
There are also books that you can get (check your library) that you can read to your child that may help them understand. I don't think this was as helpful for us as we had hoped, but it is kind of the 'easy button' if you're struggling to get it down on their level. Child educators with a background in early childhood development will typically have some good recommendations. If you need help getting some suggestions, just let me know, we have a good and reliable source.
Good luck...If you're anything like us, you'll need it.