Anywhere from 10 minutes to an hour, depending on the complexity of the story or the slowness of my brain.
I usually plot out, in vague terms, a season with a story arc. Then fill in the stories to drive it and the characters. Then actually flesh out the adventures -- usually several at a sitting to keep a feeling of continuity.
Melbourne, Australia. Winner of the First Trek Survivor Trivia Show, and Bearer of the Steve Long Pink Elephant Stamp of Learning. :)
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How much time do I spend writing? None!
Hw much time do I spend thinking about the next story? Lots!
I don't generally plan my stories too much. What I do is I come up with a story idea, or scenario idea, work out in my head what will happen at vague points through the story, then put it in front of my players and wing it.
What happens after that is anyone's guess - but at least the players can't bugger up my notes and careful plans by doing something I hadn't though of.
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"...and more controversial than Oolon Colluphid's trilogy of philosophical blockbusters Where God went Wrong, Some More of God's Greatest Mistakes, and Who is this God Person Anyway?"
- The Hitch Hiker's Guide to the Galaxy, Douglas Adams (dec.)
It depends on the episode. If I have a strong visual or other element that can support the story, I've thrown together outlines in as little as an hour or two. Outlines, for me, include the basic gist of a scene, plus any dialog or evidence that has to be presented just-so.
But it's also not unusual for me to have two or three story fragments percolating on a back burner. Sometimes they evolve into adventures; some of them are completed on only a short-story level.
Add to that the occasional tinkering around with stuff like Bryce and other programs to generate graphics. Doing flat-art for PADDs and tricorder readings is easy; creating landscapes or 'you see this' scenes in Bryce is a little more difficult and time consuming.