Over at Zelda Informer and Zelda Universe they were able to put together a possible storyline for Skyward Sword based on what they have seen so far in the game. Keep in mind that this is just information from show floor demonstrators and may not actually be the true storyline behind the game. So far what we do know is only stuff for the beginning of the game so most chances they maybe more to this story that we actually know. Jump inside to see the story that they pieced together, this story contains spoilers.
Below is the story that Zelda Informer has on their site

Link and Zelda live in the land of Skyloft, high above the surface world below. One day Link participates in a bird riding competition as part of a festival celebration. The winner of the competition gets a prize from Zelda. After winning the prize, Link takes Zelda out on a date and flies her over the clouds on his bird (okay, so the game’s probably less ‘high school’ about it, but I figure this gets the point across). That’s when disaster strikes.

A giant tornado appears, sucking Zelda down to the surface world. Link gets charged with rescuing her and receives his traditional green garb as well as the titular Skyward Sword. It’s at this point that we meet the sword’s spirit companion, Phi – she’ll guide Link as he journeys across the surface to rescue Zelda.

From there, Link travels down to the surface and enters the Sky Temple (the demo dungeon), where he suspects Zelda is hidden. After fighting through the traps, he encounters Ghirahim, the Demon Lord who rules the surface realm, who states that he and his tribe – yes, he’s not alone – are after Zelda. You duel him, he escapes, and the adventure continues from there…

Later on we will have a possible storyline for the game up in our Skyward Sword section. Keep checking back to see our storyline.

Source: Zelda Informer