Start with an idea of what you want your story to be about. This can be anything--the squirrel you saw in the park today sitting at a bistro table, the new guy at work who didn't seem to realize he was still wearing his pajama top--the choice is entirely up to you. Writer Randy Ingermanson suggests writing a single sentence to get started and then slowly begin expanding on this sentence to bring it into paragraph form. In deciding this idea, you are likely to have already started to define your main character and your primary setting (the squirrel and the park or the guy and the office).
Decide what the main points of your story are going to be. As you decide this, you will likely begin defining the main conflict--the squirrel is trying to get some food, the man is trying to hide his homeless status--and perhaps several minor conflicts that prevent your character from achieving his goal. Perhaps the squirrel can't get any respect because he's a rodent or the man must try to sneak into the office early in order to get cleaned up in the office bathroom. Jennifer Stewart with Write 101 suggests starting with the conflict, but either way works--whatever gets the ideas flowing.
Discover your main message. Every good story has a message to send to its audience. Many stories have more than one message. The number of messages you can send depends on how long your story is going to be and how adept you are at harnessing words to convey meaning. Edgar Allan Poe, for example, was a master at making every word in his stories count for something.
Begin writing. Now that you have an idea of your main character, his primary goal, major conflict and lesson learned, you can begin writing what happens to him. Every story has a beginning, middle and end. Writer Peder Hill provides some good discussion of what each of these stages entails. The beginning brings the reader into the story by letting them know the setting, the main character and something about that main character. It transitions into the middle as you introduce your first plot point--the first challenge your character has to overcome.
Develop the middle of your story. This segment of the story is where most of the action occurs. Your character faces a challenge, he works to overcome it, perhaps he is blocked or fails in some way. He must overcome this sense of failure to find another way out. Things gradually become more complicated, more intense, the pressure is building until you get to the climax--the major problem to be solved. When your character discovers a way to solve this problem, the middle is over and all that's left is the end.
Finish writing your story. Just because the problem has been solved doesn't mean you're off the hook. You have to let your readers know what happened to the various characters you've introduced them to. Lessons that have been learned are carried out. The squirrel knows how to find food more reliably, the homeless man has discovered some new survival techniques or a home. Hill points out that retaining your audience's attention after the climax is very difficult, so the end should remain short and to the point. Wrap up any loose ends and get out.