Okay, here's how I do it. It's a little bit of what everyone else already said, just combined in my own way.
I...
Yeah it sorta starts like that. I start, and then I can't think of anything to write. So I calm myself down. I sometimes like to start with the title. That works.... hmm, yeah, almost never. Okay, so... What the hell am I writing? Let's start there. And I get that little piece in my head, that very short summary of the story. One sentence, if possible. Never more than a short paragraph.
Then I go to bed, and dream. I think about it all night. When I wake up in the morning, I have a story, usually. The trick is just remembering it.
Then comes the hard part: actually getting it written. Sometimes I'll hurry and write a quick outline of what I dreamed. That helps me keep track of important details and plot flow. And usually I'll follow it. Next, very important question here, is deciding who is the best person to tell the story, who will do the narration? It's not always obvious. But, my most important writing decision is casting the characters. I spend... Well, maybe not a long time there, maybe not a huge amount of effort, but in my opinion, it's probably the most important part of my writing process. Second most important, for the fantasy I dream up is probably the key ingredient to a good story.
Once I decide on my characters, whoever they are, whatever they are, whenever they are, I give them some background. Names are always a good start. Families. Places to live. Quirks. Usually they come with their own set of predefined quirks. Beware if you ride my bus regularly, you and your quirks are probably in one of my stories somewhere. And sometimes I have to go back to bed and redo the fantasy, once I know who's in it. Sometimes that changes things a little.
Finally, with the story well in mind, I hand it over to my narrating character, along with my fingers for typing, and let them take it from there. If I'm lucky, the story writes itself. If not, it usually means I missed a step.
And then, my favorite part: when you come to the ending, stop writing.
After that, edit. Proofread. Edit. Put it away for awhile so you can come back and see it with fresh eyes. Edit some more. Have someone else read it. Edit. Take a deep breath, cross your fingers and pray it's not a disaster as you click SEND.