I would say if you want to publish short fiction, literary magazines would be the way to go. There's a website called Duotrope.com which I've found to be a great resource. It's basically a database of the short fiction market; to find the magazine (or website, in some cases) that's the best fit for your work, you just do a search based on any number of criteria (genre, word count, pay scale, etc.) Each magazine will have its own requirements for submission, but most of them will allow you submit work for free and will respond (eventually) to your submission.
Hope this helps, and feel free to ask more questions about publishing if you'd like. I wouldn't call myself an expert, as most of my stuff still gets rejected, but I have had work accepted also. It can be tough getting started, though. Good luck.
Michael

I've always wondered that (how to get short stories published). I love writing flash fiction, but what publishing company would want to publish a little book of short stories?
Do magazines print them? If so, how? Do you just send them in to any magazine company and see if they get accepted? Or newspaper?
Obviously, I really don't know much about how this whole system works. If anyone does know and would be able to help me/tell me I would really appreciate it!
Thanks