Tell the child that the dog was broken and couldn't be fixed. Let the child see you dig the hole and even help to dig the hole. have a "memorial" service and let the child say the best thing about the dog. Put the dog in the hole and let the child see you bury the dog with its favorite toy. The child will ask questions on its own. Answer them truthfully and simply.
Just be honest with the child. My almost 7 year old has lost 2 friends to death in the past year. One of her friends was only 4 years old the other her same age he was in her 1st grade class. We are Christians and so we told her they are in Heaven.