Readers of short mystery fiction look for instant gratification. They're not interested in complex philosophical ideas about good and evil or the nature of the human mind. That doesn't mean, though, your imagination has no room to play. Here's how to write a successful mystery short story.
Read some mystery short stories to get the feel of the pace. Edgar Allen Poe and Arthur Conan Doyle are the masters of this genre. You can even find some of their short stories online at Project Gutenberg (see Resources.)
Decide what crime has been committed. Know the criminal's motivations by exploring his psychology. Write a detailed character sketch of the person who solves the crime, especially if it's a detective or amateur sleuth you want to build a series of stories around. Make your detective or amateur sleuth have some distinctive qualities. For instance, Sherlock Holmes was an intellectual obsessive who used cocaine and dressed a certain way.
Draw a map of every setting in your short story. Make a character list so you know your suspects and their potential motivations. Write a detailed description of the crime so you can insert red herrings later.
Make a list of the other major scenes leading up to and winding down from the crime. You'll likely be surprised by details you didn't plan to include when writing the rough draft, but you should have at least five major scenes to hang your story on. It's best to limit your mystery short story to one crime.
Join the Short Mystery Fiction Society (SMFS.) Their discussion list has an international membership who can answer questions about story details like setting and crime technicalities.
Write the rough draft of your story. Be as wordy as you need to be at this stage. Make notes in the course of writing it about details you didn't plan to insert. It's vitally important you take care of them all by the time your reader reaches the end.
Set your story aside for at least a week. Read it again from the perspective of someone who doesn't know who the culprit is. Do this multiple times until you feel it's as good as you can make it.
Share your mystery short story with a writer's group. Brace yourself for honesty about whether your ending rings true. Nothing is more irritating to a reader than a mystery that falls flat.