I've never had much luck submitting short stories to literary journals for publication, thought honestly I haven't tried very hard or submitted very many since I was in college. Strange to say, I've published more novels than I have short stories. I once had a story come in as a finalist for the Indiana Review and Iowa fiction awards, but that's about as far as I got with even that story. There are a dozen factors in getting your story published in a journal, from how good your story is to the taste of the editor (or assistant) that reads it to the overwhelming competition to place a story in general. For several top journals, and even mid-tier journals, the acceptance rate can hover around 1%, or less. For every novel that gets completed, there are probably a hundred or a thousand short stories written, many in workshop programs that can only fit in short stories due to the unwieldy nature of an entire class trying to workshop a novel.
If you're interested in submitting short stories for publication, I found this Manuscript Formatting document on William Shunn's website. I'm pretty sure I did some, but not all, of this correctly back when I was submitting regularly, and having an official looking submission can only help your chances. There's also Duotope's Digest to help guide you in your submission process.
Or, if you don't care about placing your stories somewhere and just want them out there for public consumption, you can just go the route I've taken and put your work up on scribd.