You finished your story. You submitted your story! Now what happens?
Each market handles submissions differently. You can probably find information about your particular market’s process via their website. But, let’s be general.
For most submissions, your story will enter the Slush Pile. The Slush Pile is the accumulation of all the submissions a market gets. Generally, a First Reader / Slush Reader will look at the story in the order they’re received. First Readers are tasked with winnowing out the submissions. Some will be looking for folks who followed the submission rules, and others will be giving a thumbs-up or thumbs-down on on a particular submission before passing it up the line.
Submissions then go to an editor. The editor will either pass on it, or pass it up to an Editor-in-Chief for final determination. Your mileage will vary (so will your response time).
At any point you might get rejected. This happens, a lot.
Strange Horizons offers a very explicit view into their process. You can see it HERE