I think the main process of writing is the writing itself.
It's not the preparation.
It's not the note-taking before.
It's not the task of improving what you've written down by exchanging words and phrases over and over again.
It's the action of writing. The movement of the pen. Your fingers pounding the keys on your PC/Mac/laptop. The fluency of thought you experience.
Try it now: Take a pen. Take a sheet of paper. Write.