What is the best most sensitive way to tell someone their child has died?

Be honest. The best method is to be honest, display empathy and allow the parents to dictate the conversation- ask them how much detail, information they want to know right away. Let them be alone if they want, cry, scream, get anger or show whatever emotion they need. Don't say you understand- because you probably don't.
It varies. I don't think there is any one way to convey the bad news. I do it by using soft tone of voice, expressing empathy, but yet telling the parents the truth. I also pause for a moment or two for them to go over the first shock. I also ask them if they want to know more or we should part for them to think about what they want to ask.