Plan.
Before taking the plunge (or shortly thereafter), it may prove invaluable to sketch out a plan: where you'd like the story to go; what will happen; an outline of major characters and their traits, if applicable. This will help you focus and down the line, when it's time to edit, will allow you to compare the list against the finished product to see if you did what you set out to do. The objectives of your story may change over time; this evolution is absolutely fine, and a list will help you keep track of that process. A story plan will help you understand your own motivations as both a writer and a reader, and help you get started by illustrating the big picture.
Move While the Mood Is On.
The best way to begin a story is in the heat of excitement -- right after you conceive the idea. It's at this time that writing will appeal to you most, and you'll be motivated to write while the idea is fresh. Though you may well think about the story extensively later on, it's easy to become bogged down in detail (and even rewrites of drafts that don't exist). It will be easier to spot your story's strengths and weaknesses on paper. Later, when the fire of creation still glimmers but doesn't rage, you can read it with an objective eye and edit in disinterested fashion. The idea is to capture the essence that inspired the story's idea.
Open with a "Tantalizer".
Consider opening your story in the midst of a conversation. It's not a must, but the dialog opening is a valuable addition to a writer's toolkit. Beginning a story with dialog must be done carefully: while a reader does not want to be thrust into the middle of a confusing, dull or irrelevant conversation, opening with provoking dialog can be a winner if it does not disorient.
The reader is given a window into the action as it unfolds from the perspective of those involved in the conversation. The pacing is lively and is not weighted down with the heft of plodding description or backstory.
Dialog isn't a must for the opening. Capturing the reader's attention in the first sentence is.
Experiment.
Famed author P.G. Wodehouse often plunged into writing; many times, he noted, the story went in an entirely different direction than his beginning, and that start was often completely lost as the story evolved. Experiment with different openings to see what works best. Ask yourself which opening represents a story you'd like to read. Try not to get caught up in ideas about what you "should" do; choose an opening that appeals to you as a reader.