I think it's worth pointing out to someone who has never played a Final Fantasy game before that the games are not all a part of one continuous story. For example, you don't have to start with 1 and play all the way through to 14 in numerical order. The stories of the games are completely unrelated, except for the sequels and prequels, which will still have the title of the original game with them. (For example Final Fantasy X-2, Crisis Core Final Fantasy 7)

As for the story of this game? I've recently made a thread with a link to a song about Final Fantasy 2. The lyrics describe the story of the game, so check it out if you don't mind spoilers

FINAL FANTASY II (with PelleK) - YouTube