The rules are in no particular order, so I haven't numbered them. Please do let me know if bullet points aren't enough and you would prefer them in numerical order of importance. Onwards!
Try not to feature too many characters
[The last short story I wrote had three main characters and two prominent supporting characters. I wanted it to be a novel, really, which is why it will probably never see the light of day as a short story.]
You don't need to resolve everything
[I can think of a number of strong examples that disprove this rule, but I don't think any of them would have been harmed by following it. So... I stand by it.]
Know what your characters want (at the very least)
[In the first short story I had published, I knew nothing of this but subconsciously, I had a very clear idea of the main character's motivations, so it worked. It does not always work, believe me. Eventually, it will become automatic, but until then it's something you should force yourself to remember.]
Tell a story
Which is my way of saying that you should structure your story like it's a story (see handy diagram). This is called the Five Act Structure and was invented by some guy called Freytag. It's a perfectly good structure to follow and, to all intents and purposes, still allows for an infinite number of story possibilities. However, in a short story, the Exposition bit should be super short, if non-existent, because you don't have time to waste. You should, really, begin at the point of Rising Action, though sometimes a little scene setting is required, so I will be lenient and say that you don't have to if you don't want to (but you should). There is also the Three Act Structure, which was invented by Aristotle and is comprised of the Setup, the Confrontation and the Resolution. Everything I said above still holds, but with two fewer acts.
[I find structure the hardest bit about writing but this is likely because it is probably the most important aspect of story telling. You should always be thinking about it, even if it's not a predefined one like I've given above, you can't just put the words down in any old order. Unless you're writing a blog. Self-zing!]
Try to get it published
You might as well. You also may as well try to get it published by the most well-respected, high-profile publisher of the kind of short stories that you write. If it's literary, for example, just send it to Granta Magazine. You never know! And then when you have experienced rejection (which will lead to most excellent personal growth), try other publishers who are more willing to take a punt on a newcomer. It's best to go for the ones that pay, but not vital (or even possible, depending on what kind of story you are writing), and I think the joy of getting published will doubtless override... um... poverty.
[Please see previous post for depressing news about writing short stories.]