What do you write?
I imagine the techniques for coming up with stories vary from genre to genre.
I write fantasy. when i sit down to think through a fantasy story, i focus on four basic elements: magic, setting, plot, and characters.
usually, i start with a wrold or an idea for a system of magic, and build the rest aorund it. with my most recent story, i came up with a means of working magic, then a person who does so, then a situation for him ot be in, then the place where it all happens. other times, i've started with a character, like a rebellious angel, or a setting, such as a real-world college, but with magic.
Another tactice i've found useful is to take a hard lookat the cliches of fantasy. i'll often take a couple and mash them together, or rethink them so that they make mroe sens eot me. for instance, I don't really like the whole "predestined hero" charcter, so i decided to write a story about a "chosen one" who just gives up and goes home, abandoning his purpose. eventually, i decided that the prophecy would be a manipulative lie.
I imagine that a mystery writer would start with the crime (or the detective) a romance writer would start with the main characters (or just the nature of their relationship), and so on.