I usually write at night, and occasionally into the early morning, though this becomes a problem when I have to get up for work. However, I find myself constantly thinking about my story, no matter what time it is. Thankfully I'm able to remember most of my ideas until I get home, though I occasionally scribble notes on paper towels

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I always write in a notebook, something about the computer seems to "formal" to me. I find that my thoughts flow easier when I put them on paper. I also prefer to cross out my corrections instead of deleting them, allowing me to go back later and see what I've omitted.
I'm most comfortable writing when I'm spread out on my couch with my dog napping somewhere nearby. Thankfully, I live alone, as I remember quite painfully how difficult it was to concentrate on writing with a house full of people constantly moving around.
As for music, I absolutely can not listen to it as I write. I need silence. I guess that's how I got in the habit of writing so late at night.