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You could publish it on wattpad.com. That website is not too professional exactly, and in my opinion is mostly just filled with teenager romance stories, but it's a good place to start. There are other websites that even offer you a printed version (like a real book version...with glossy pages and everything) of your story. I forgot the names of those websites, unfortunately. It depends on what you're exactly aiming to do - publishing your stories for the enjoyment of other people and getting feedback, or something else. Cheerio! :) P.S. lovely funny piece of writing there. i especially loved the way it ended.
Have you ever heard of inkpop.com? Better check it out or something. I have a few friends who would post it up there, and every month, the top five books would be read by the Ink Pop Editorial Board. The best of the best would be sent out for publishing. :)
I didn't read your attachment just yet, and I'd get to it as soon as I can to give my own critique. Hope this helps!
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Sorry, correction. The Editorial Board (which I discovered to have HarperCollins editors, wow!) would review it, and there is a possibility of being published. Technically, members of the site would "Pick", the website's equivalent for voting, the books they like. If your writing is extremely publish-worthy, the more popular you will be to the community, and in turn the higher the chance you'd have of getting published/recognized.
Being a successfully published writer is a toughie, love. But you got to start from somewhere! Much luck.
Getting published in magazines and other periodicals is very, very difficult. Magazine editors are very picky about what they print. Not only must your grammar and spelling be near perfect (the occasional typo is okay, but blatant spelling errors will get the piece thrown in the trash), it must be very engaging. Also the more high profile the magazine is, the harder it is to get published in it. Playboy for example will only publish already established authors.
If you are not dead set on being seen in ink, electronic publishing would be the way to go. Blogging is your best bet. You can never be rejected from your own blog, gaining readership can be tough though, but that's another matter there are plenty of articles out there on improving your blog traffic if you Google it.
You could also submit to writing sites, as has been suggested.
A third option would be to self-publish through one of the various eBook sellers. This can be difficult as well, but not as hard as getting a magazine to accept your work. You can find plenty of info on publishing eBooks if you Google it as well.