How does the narrative structure of "There Will Come Soft Rains" communicate the author's message?

There are a number of ways in which this question could be answered, but I would want to focus on the way in which this story presents the level of technology in this future world combined with the absence of any human figures. One of the amazing aspects of this tale is the way in which we are presented with a house that is so technologically advanced that humans are not necessary for it to continue in its duties. It is completely self-sufficient even without its owners, as the following quote makes clear:

Eight-one, tick-tock, eight-one o'clock, off to school, off to work, run, run, eight one! But no doors slammed, no carpets took the soft tread of rubber heels. It was raining outside. The weather box on the front door sang quietly: "Rain, rain, go away; rubbers, raincoats for today..." And the rain tapped on the empty house, echoing.

What is notable is the extremely sophisticated level of technology in a setting where the only mention of humans are the dusty "silhouettes" of the family that once lived in this house, who have obviously been wiped out by some sort of nuclear attack. Bradbury thus forces us to ask ourselves harsh questions about our level of technology and our cleverness. The same technology that is responsible for this amazing house is also responsible for the weapons that eradicated humans from the planet. What is the use of such cleverness and ingenuity if we do not have with it the humilty to accept our fragile and vulnerable position in our world? What use is our technology without the wisdom to use it wisely?

Which narrative technique advances the theme in "There Will Come Soft Rains"?

The narrative writing technique that most develops and advances the theme through the course of the text is personification.

Personification, as shown most clearly in the automated house, is used to drive home the point that machines now control humans. Humans originally created machines, but in a classic example of the tail wagging the dog, it's technology, in the form of nuclear weapons and automated homes, that is firmly in charge.

What's particularly ironic about this is that there are no human beings left in this postapocalyptic landscape. Personification, therefore, cannot apply to anything but machines such as the automated house. And so it should come as no surprise when Bradbury uses language in describing the house that would ordinarily be used to describe human beings, such as when he refers to the house's "bared skeleton."

But as these words show, the automated house, though still a person, is far from being well; appropriately enough, given the barren, war-ravaged landscape it inhabits.