I usually carry paper with me in my pockets all the time. Whenever a thought comes to mind I jot it down. These "scribbles" are taken out at the end of the day and tossed onto my rolltop desk. I am an early riser, and 4:15 AM, enjoying my morning coffee, it has been my custom to go through the stack of scribbles and type them out using Microsoft Word. The various sentences then become embellished paragraphs and usually cut & pasted into whatever "story" they seem most compatible with. Thus far over these many years, 15+ I am working on at least six different novels, poems and genealogies and a religious research book.
I then go through these rough drafts and re-work them internally, cut and pasting, adding and subtracting, and embellishing the thoughts into a plot, hopefully with more than a few twists in the end. When doing the character's dialogue I usually just write out the conversation straight out. Then I go back and add the "he said" and the "she says". It is fun and challenging to have the dialogue sound positive and the body language negative or vice versa the other way; she smiled and said, "I can't stand you." Makes for more interesting and realistic character developing. A lot of times by doing this even I am not sure how the characters are going to develop. On main male character made "look like" a real life person I know, their mannerisms are those another person I may know, they "sound" like a third person and their personality is of yet a fourth person I may know.
Along with all of this, I sprinkle in the time of day, seasons, surroundings; which all play into the mood of the character and helps to push the unfolding story along as well. I like twists and having an unexpected, devil's advocate of an ending; and then "watching the reader's face" - I didn't see that coming - is the fun part.
Well, this is how I craft my story process. I am not sure how others may do things, but it's how I've been doing it and the writing has become a great release for me. Hopefully, readers will enjoy the efforts of the sharing.