Think about your story before you write it. Consider how the plot will unfold and how it will affect other characters. Here you need to get a general idea about what your story is all about. If you want to prove a particular point or make a particular statement, make sure most of the plot elements revolve around this.
Grab a few sheets of paper to write down all of your ideas before you begin. Write down the general skeletal timeline/outline of your story, especially for longer stories. Write notes on the scenes, events, characters and setting to help flesh everything out. See the resources section for a tutorial on creating your characters.
Begin writing; do not worry about editing. In fact, just keep writing and do not look back. As Sean Connery says in the movie "Finding Forrester," "You must write your first draft with your heart. You rewrite with your head." If you are writing a longer work, this becomes all the more essential. Doing so will help move the story forward and get you closer to actually finishing the story. If you go back and edit before finishing the rough draft, you may lose yourself in all the errors that a rough draft naturally possesses, crippling your progress.
Complete the rough draft and set it aside for a few days. If the story is novel length, set it aside for a longer period of time (no more than a month). This way you'll forget about certain parts of your story and can approach it much like a reader would.
Read over your story, a few times.
Look again at your notes and compare it to your story. Make note of the things that further the intended subject and idea as well as the things that stray away from it. You need to tighten these areas and remove them accordingly. Even if a particular section reads very well and you're really proud of it, you must get rid of it if it does not contribute to the theme or the story in a significant way.
Edit for these plot points and themes. Keep strengthening your story.
Edit for grammar and punctuation.