My ideas come in bits and pieces -- interesting scraps that combine surprisingly well with something entirely different. I read a book on writing SF/F (the one by Orson Scott Card, I think) that talked about how sometimes you can combine really disparate ideas to make a really good story. This is a technique that's worked very well for me when I've had an intriguing scenario but no plot or characters.
Here's the patchwork quilt story of my first novel. (FYI, my first two novels, Fires of the Faithful and Turning the Storm were originally written as a single book. When Bantam bought it, they split it into two books and had me expand them.)
During my junior year of college, I had a dream in which I was called home because my grandmother had died. ("Home" in the dream was not my real home, but a farm on the outskirts of a small village.) I arrived, and things were extremely strange, but no one would tell me what was going on. My grandmother had left me her violin; I knew, somehow, that she'd left me an important message hidden in the sheet music, but couldn't figure out what it was. Then some sort of storm started; I ran outside with the violin and started playing, looking up at the tornado funnel above my head. I knew it was a supernatural storm, not a natural one, and that as long as I kept playing, we would be safe, but if I stopped, we'd all die.
I woke up, thought that this was a dream that clearly needed to be made into a story, but couldn't come up with a good secret that the grandmother could have tried to communicate.
This same year, I had taken up violin. I had taken piano lessons starting when I was five years old, and had given them up my senior year of high school, because I would have had to commit to a lot of practice time in order to make any progress. I never had any interest in being a professional musician; it was just a hobby. In college, I decided I'd like to learn to play the violin, so I took it up and was a fairly proficient beginner by graduation.
When I'd go into a practice room, I'd often be able to hear someone practicing piano next door. If they were an advanced student, they'd often be playing a piece that I'd played in high school. Hearing that always gave me a rush of wistful nostalgia: I could do that again, if I had the commitment. It made me meditate on the choices we have to make. And since I'm a fantasy writer, I started thinking about writing a story about choices, but with a fantasy setting -- someone who'd had to choose between music, and magic.
In mulling over the story, I thought about the idea of magic having a price, and thought, what if the cost of magic was environmental destruction? After all, if technology is our magic, that's kind of the cost of magic in our own world.
And suddenly, I had all the pieces for a short story that was going to rock. I wrote it that summer. Etienne (who was female, but this male French name sounded very female to me) was a student at a music conservatory. She got a new roommate, Misha (also a male name -- don't ask me to explain why), who had a deep, dark secret. At the end of the ten-page story, it was revealed that Misha was a runaway sorcerer, hiding the secret that the use of sorcery was causing a famine. It was (in my mind) an absolutely brilliant story, the best thing I'd written at that point. I sent it around to several magazines, and collected a number of rejections, including two that noted that it read more like chapters one and twenty-six of a novel.
So when I decided to write a novel, I thought, well, since I already know what happens, I guess I'll try writing that one. I made a couple of false starts that tried to re-use the short story as the first chapter, and then just started over from scratch. In the finished novel, the part set at the conservatory is 100 pages long. I had to rewrite the beginning several times, as I learned pacing, but "how I wrote my first novel" is a post for another day.