In On Writing, by Stephen King, he goes into great detail about his writing process.
The upshot is that he's what some writers call a "Discovery Writer", he sits down at a blank page with an image, or rough idea, and just writes and sees what happen. (George RR Martin/Game of Thrones is also, believe it or not, a discovery writer).
I'm not familiar with Asimov's process, but based on Agatha Christie's genre, I'd be surprised if she didn't structure hers fairly heavily.
