I've been getting short stories published for a long time. More than I can even count now. I've done this without an agent and I've always managed my own career.
The one common factor in getting short stories published is searching out calls for submission. This is how I've always done it. And it's the way every other unagented writer I know has done it.
You can find calls for submission on publisher web sites, like this one right here. Cleis Press is not the only publisher who posts calls for submission. It's your job to do the homework.
You can also find calls for submission posted in mass form right here. Then you click "Erotic Readers and Writer's Association," which leads you here. From there, you scroll down the page and on the left hand side you'll see "Author Resources," which takes you over here. After that, it's a plethora of calls for submissions, all from which you can pick and choose.
I also know that small e-publishing presses are always looking for calls for submission. Ravenous romance posts them here all the time.
I also just read on facebook that Silver Publishing is posting calls, right here, under "Special Submissions."
Speaking of social networks, I've seen calls for submission posted on both facebook and twitter. But you have to catch them when they are posted, so I think it's better if you do the footwork on your own. It will keep you more organized.
These are just a few. There are many more and it's up to you as an author to scope them out and figure out where you want to submit. Getting pubbed in an anthology with a short story is fun and it will give you a few great publishing credits.
And all you have to do is write a spectacular story and submit it by following the specific publisher guidelines. Submitting fiction is nothing like submitting non-fiction, so pay close attention the the publisher guidelines.
There's nothing more to it than that. I swear. I've been doing it for almost twenty years.