I ask myself questions about the structure of the story I've written (is there a structure, is it strong enough to take the plot created and so on). I ask myself how I would react to the story if I was buying it (in a magazine or a book, online or in print)? I also ask myself if I would buy the tale if someone else had written it this way?
I check for the sense of the story, spelling, grammar and so on. I also ask myself if there was anything I could have left out, anything else I need to add in? And it is at that point I start getting my story out there!
How your characters react to being questioned can also be insightful. And who plays the role of inquistor here? Is their role accepted or resented?