I've been told that I am a great writer many times by friends and strangers who have read my short stories. I was wondering, how do I go about getting my works published? I'm not sure where I should begin to showcase my talents.
You should start by finding as many web sites, publications, email lists, and books that list calls for submissions. I don't know what kinds of stories you write, so I can't give you specific places to look, but there are writers associations on the Web, magazines like Poets & Writers, and lots of guides and lists with calls for submissions. Research what kinds of publications-magazines, anthologies, etc.-have published work like yours, and find out if they take unsolicited submissions. Sometimes you have to write a query letter first; other times, you can send a manuscript right off the bat. Be sure to follow the call for submissions or the writer's guidelines; as an editor, I get so frustrated when people don't follow the simplest instructions (like, no email submissions, or enclose a self-addressed stamped envelope). Take the plunge, and send your work out into the world!

