It depends on the inspiration, I think.
It can be a song, an scene, a character, etc. For the thing that I am doing right now it was a concept, and I started building around that concept. What could happen, what should not happen, etc. Then I saw the common points and developed some characters for those stories. Later I saw how those characters personalities would affect the overall idea already thought, and make it beleivable.
Finally, when the thing took shape in my mind, I wrote the big arcs in one paragraph. Later in an excel I divided those paragraphs in chapters, later I revised the excel to add a better flow to the whole thing, and lastly I wrotte a word file with one chapter, dividing every page in a couple of sentences, sometimes with script, or just the idea, with locations characters and everything else that can be useful. Just then I started the comic. That for the script, the drawing have a whole other process xD
For drawing, I use to check other peoples works, search images on google for reference, and once I settle on style and overall characters concept, I start practicing a bit until I feel confortable drawing the charas. It doesn't matter though, as I learned very quick that once your start working on your comic, your hand learn new tricks on the way and in just a couple of chapters your style will improve and your old chapters will look cheap compared with your last piece. I resist the urge to draw everything again xD
Also I learned that once I start making a chapter, I must change some things depending on if the scene feels real, and go back to the excel or word to add the new information. As the process is fluid, and the grounds are solid, I can make those changes without affecting the overall work.