The first way to tap into your "inner writer" is to read what others have written. Many prospective authors find it helps them discover what it is that resonates best with them -- what it is they love. Kurt Vonnegut's prophetic "Welcome to the Monkey House" is an award-winning collection of short stories that spans a wide array of genres -- "Harrison Bergeron" and "The Euphio Question" are two short stories that may inspire you.
Let's say you want to write a science-fiction short story about dystopian society -- a futuristic world where Wal-Mart is no longer a retail chain, but a new branch of government; citizens live in a utilitarian hierarchy and so forth. You can build a solid fictional landscape by generating a series of drafts or outlines with character histories of important players. Build character profiles with detailed information about each character, including full name or nickname, height, weight and body-type. You can also incorporate detail about personal history such as religious background or political leanings. You may not use all the information from the character's profile in the story, but it will benefit you as the writer to know as much as you can about your character.
Audiences tend to identify with characters who have personal idiosyncrasies such as a tendency to keep a dirty house or swear profusely. When naming your characters, borrow from literature archetypes; if you have a character who is especially sinister, name him Mr. Grimes, for example.
Dialogue is often a problem for new writers. The best way to make a story conversation flow is to actually speak the words yourself. It may sound odd, but you can work out any rough spots in most exchanges this way. For example, imagine a man sitting on a bar stool in a just-about-empty cocktail lounge. A woman walks up beside him, then drops her purse into his lap. There are dozens of ways the story could progress from this point. Act out the words you believe someone would (or would not) say next.
One of the best hints on writing short stories is to understand there is nothing you do that cannot be undone -- if what you write doesn't work for the story, rewrite it. A wonderfully sublime aspect about writing is that it is entirely subjective -- you cannot get it wrong. Writing is a form of self-expression and no one can fault you for what you feel. You can decrease your frustration by understanding that learning how to express yourself is not something that comes automatically for most people.
Writers have a tendency to throw their writing away prematurely. Once frustrated, they want to be rid of that "horrible" thought as soon as possible. You have to remember, the object of writing a short story is not to judge what you write, but to express -- you may not be able to fully envision a project during a fleeting moment of difficulty, so save that so called "lousy" piece of writing as you may find good use for it later.