I assume you want an honest answer without any sugar coating. The odds are against you. Even smaller publications usually have giant slush piles and your manuscript is unlikely to grab their attention.

That being said, the only way to get published is to submit work. If you're already writing fiction, you might as well try to get it published. I would first recommend learning how to write a proper query letter. This will increase the chances of grabbing a publisher's attention at first glance. As far as finding publications, Duotrope is a quick and easy way to sort through various magazines and journals by genre, required length, compensation, etc. I would also recommend the Writer's Market, a book that is published each year and contains an invaluable list and descriptions of almost every publication you'll ever need to be aware of.

After narrowing down the throngs of potential buyers, read a few pages of each remaining magazine/journal/website, and take note of style, content, etc. This will give you a good idea of what they're looking for.

If your fiction is to be published, it must be excellent. Give it to friends, family, whoever, to read and critique, only submitting it for publication when it is thoroughly polished. (Do not post it here, unless it is a link to a Google Doc or something similar, otherwise you will have nullified the first publishing rights required by many publications.) Publishers do not want the responsibility of editing your work. They'd much rather find a better piece from their overflowing pile of submissions.

Good luck.