When I was younger, I would just start writing with whatever was in my head at the time. I'm a bit more premeditated now. I start by creating something I think of as a story seed. A story seed needs at least three things:

1. an interesting character,
2. a situation that challenges the character, and
3. (since I write fantasy and sf) a speculative/fantastical element or idea

The first two are pretty standard ingredients for launching plot. The third is important to me, because I like the imaginative elements of fantasy or science fiction to be integral to the story. I don't carry to read a detective story that just happens to be set in outer space, or a romance where the characters just happen to be elves. I want the imaginative element to be important enough that the story wouldn't hold together if I left it out.

I keep an idea file where I jot down thoughts about characters, situations, and speculative elements (along with settings and themes). That gives me some raw material. But I don't start writing until I'm sure all three parts of the seed work together. It can't be any interesting character in any challenging situation. What makes the character interesting has to be matched to the situation somehow. Maybe the character is especially suited to the challenge (or, more interestingly, especially unsuited to it). Maybe the challenge emerges from the character's personality.

I also want the sf/fantasy element to connect with both character and situation. A powerful magic that can be used only by someone in a peaceful, meditative state is not much on its own, but paired with an impatient, talkative character brings it to life.

I do a lot of work in the back of my head before I decide to start writing a story. I need the three elements to click together, and I keep trying on different possibilities until I find a combination I like. Even while I'm writing one story, I'm playing with the seeds of others.