Pretty much the same goes for stories as it does for poetry. Pick up a pen or open a word processing document and write. Your first draft will form the basis from which you can add bits, take away other bits and work on things like plot, characters and dialogue. Everything we write needs a beginning, middle and an end so get an idea of what yours will be and write it down. This is your outline and will give you some direction and act as a reminder for where you want your story to go.
I can't suggest strongly enough how useful it will be to pick up a few books on writing fiction. Plot development, characters and dialogue takes planning. Books on writing abound so start at your local library until you get a feel for what you want. Stephen King's "On Writing" is popular, easy to read and understand, and inspiring. There are hundreds, if not thousands, to choose from.
Join a writing group; online if you're a bit nervous about real live people. Check as many out as you can first and go with the groups that sound the friendliest and helpful. Another form of writing group to consider is via fan fiction. Fan fiction is fiction written by fans of television shows and movies. The stories in these groups go where the screen versions don't go. You can usually pick up a few beta-readers or editors connected to the group that will help you develop your story or, at least, point out grammatical, punctuation and spelling errors.
If you're worried about spelling, word-use or any technical aspect of writing, there are books to cover that as well. Start with a dictionary and thesaurus. Next consider a book or two on word usage. That is, something that explains the difference between words such as "lay" and "lie", when to use them, etc. Bill Bryson's "Bryson's Dictionary of Troublesome Words" is a good start.
If you have a growing pile of short stories that have been polished as close to perfection as you can manage try submitting them off to a few competitions. You can find lists of competition information through various writing newsletters and groups, or join your local writing centre. Writing centre's provide access to groups, courses, competitions and information for writers of all abilities. To find the one closest to you either do a web search or inquire at your local library.
You will go through stages of thinking that your writing is not good enough. You will compare it to the work of other writers and consider it lacking. We all do this at some point or another. Welcome to the world of the creative artist! Mull over your apparent lack of talent for a bit, then get over it and get back to writing. If you seriously feel you need extra help in a specific area, ask for it via a critique or writing group. Work on your weak areas and they will grow stronger.