If you peruse various writers' market websites, you'll often see anthologies open to unsolicited short story submissions. They usually have specific guidelines, are often theme-oriented (such as 'monsters' or 'tropical horrors' or 'dental horrors' etc., but often they are also just open to good, specific genre writing.
If you're new to fiction and haven't published yet, or are just starting to publish and wish to get your name more known and circulating in the field, always keep an eye on open anthologies as well as independent zines seeking work.
If you scroll back through the January posts, you'll see one with listings for some fiction market info such as Ralan's and The Market List, etc.
These lists regularly update information on markets seeking work, closed markets, dead markets, backlogs in response to submissions, etc.
When I first began writing short stories years ago (and when all stories were submitted via snail mail rather than electronically), I used to keep a hand-written log book of story submissions with columns on each page that went along the lines of:
Title Market Editor Address Response Other
When you're circulating half a dozen or more pieces of work at a time it's easy to forget when and where some things have been sent without keeping a good record of this. These days it's just as easy to use a spreadsheet or other computer program to accomplish the same thing. I just have a penchant for hand-written notes when it comes to stuff like that.
Make sure, when you sent an electronic submission that you use a proper format in your e-mail (some wish for it to be pasted into the body of the e-mail while others will accept an attachment), but ensure that your program won't scramble your spacing and proper margin justifications. It's a good idea to send your document to yourself either at a primary account or secondary account in order to see if your proper manuscript formatting comes through effectively first. As some markets will state, first impressions count, and that means an effectively written cover letter too, if required.
Some markets may ask for a short synopsis of your work, especially if it is a novella or novel. Learn how to write a strong synopsis, present tense, third person narrative POV, no dialogue that focuses on the main action points and flow of your story from beginning to end. Many good sites on the internet provide sample query letters, sample cover letters, sample story synopses for writers to review and from which to learn these necessary skills.
New markets and new anthologies pop up all the time. Sometimes, certain antho's are 'invitation only' and not open to unsolicited submissions. I don't tend to agree to that, but regardless, it is the way of things at times, but many others are open to whomever wishes to submit their best piece of work.
Check them out; they provide valuable venues for breaking into print, especially if you do have a novella or novel that you wish to submit in the future - publishing credits with small pieces do provide a platform/credibility, even though we all must start out unpublished.
And above all, keep pushing until you break through.