Don’t rely on the computer spell and grammar check solely.
Always use a good dictionary/grammar guide as well. The computer doesn’t always get it right! Mine seems to have an aversion to the word “their”, it keeps saying I should use “his or her”! Imagine how clunky that would sound in a story! See the computer checks as a starting guide only. I use the Concise Oxford Dictionary and Thesaurus.
Make sure you know your character well enough to be able to write about them. Or you’ll have no story! Or you’ll quickly reach a dead end. Some writers do a full character CV. I tend not to but do start with a main trait and take things from there. For example in Eileen’s case, I gave her the traits of awkwardness and defiance. Loads of stories can come from that!
Enjoy your writing! Or there’s no point to doing it at all, is there? Also I think if you love what you write, it will show in what you write and make it a more enjoyable read and therefore a more publishable one.
Know your market. How else can you sell your work? And be aware there are short story openings on the web, radio, small presses as well as the traditional magazines.
Proof read your own work before submitting. Try to make sure you allow enough time for this. I once sent a story off in a hurry to meet the deadline, it didn’t do anything in the competition it was entered for and on its return I saw a blatant mistake. I’d changed the name of the main character and didn’t ensure the change went all the way through the story! Learn from your mistakes and do something positive with them! I took this story, corrected it, amended it and expanded it and sent it off somewhere else that allowed for a longer word count. The amended story I feel is much better as I was able to expand the characters that much more. So something good came out of my faux pas!
Read author interviews in magazines. You can learn a lot from them and when several writers recommend writing books – for example Stephen King’s On Writing – get a copy and read it! I did – oh and I recommend Mr King’s book too!