There is a classic bit of writer's advice you will probably run into if you spend any amount of time looking for that sort of advice -- the story starts with somebody wanting something.
It can be anything, as long as somebody seriously wants it. It can be as simple as a desire to restore honor to the family name or as terrifying and difficult as trying to impress a pretty girl.
It's a basic recipe. The character's desires help define the character. The character's actions to achieve the desire move the plot along. The obstacles to that desire create conflict. Overcoming conflict provides resolution. Character + Conflict + Resolution = Story.
I was recently reminded of an interesting variation on the recipe. I was watching Joss Whedon's short musical Dr. Horrible's Sing Along Blog. It's a nicely structured little story. But it starts with a clever twist to the recipe above. It starts with a character who wants two somethings.
This simple variation opens up a wealth of possibilities. The two desires can conflict, to start with. Maybe coming closer to one goal moves the other further away. Or maybe a great opportunity to achieve the second goal arrives right in the middle of delicately timed preparations for the first goal. These conflicts force the character to constantly choose which desire to pursue. It becomes a much greater task to achieve both.
This variation also makes the outcome less predictable. The most common resolution of the classic recipe is that the character gets what he or she wants. But when the character wants more than one thing, then our hero can both win and lose. Or both goals can be achieved. Or the resolution can ultimately turn on the making of a choice as the protagonist learns what he or she really needs.
It can be argued that almost all fiction writing is formulaic. Who cares, as long as the story is good? And writers will keep playing with the formula. What comes to your mind if I say the character wants five things? That's a good start on a nested quest -- kill the ogre to get the magic sword to face the dragon to rescue the princess to save the kingdom... But it would also make a good farce. The guy who inherits a million if he gets married before the end of the month but he is juggling five girlfriends, none of which will marry him if they find out about the other women in his life...
So, you want to start a story? Tell me what your character wants.