Okay, here's what I understand so far:
In Ivalice (FFT world), Archadia and [some other country] are fighting a proxy war with each other, and Archadia is pretty much winning. Archadia invades a small country called Dalmasca (setting for most of the game [so far]). The seven princes of Dalmasca die in the invasion. A guy named Reks (I thought it was Lex, but w/e) meets up with Basch some other Dalmascan soldiers. The lot of them storm the Dalmascan castle to try to rescue the king. Reks and the soldiers hold off some Archadians while Basch goes into the throne room. After the battle, Reks also goes into the throne room, but only to discover than Basch has slain the king and his envoy. Reks is confused and asks why. Basch tells Reks that the king sold Dalmasca to Archadia and let the invasion happen. Vayne (Prince of Archadia) and his soldiers enter the throne room, kill Reks, and arrest Basch. Basch is labeled as a traitor in Dalmasca because he killed the king.
Two years later, you take control of Vaan. Vaan is an orphen & pickpocket on the streets of Rabanastre (Dalmasca's capitol). The country is now run by Judge Ghis. Vayne arrives and makes a huge speech. (My Japanese sucks but basically he says stop fighting.) Vaan meets up with Penelo afterwards, and goes down to lower Rabanastre aftewards (the sewers).
I've got that much figured out. I know sort of what happens, but not entirely...arg my Japanese SUUUUUUUUCKSs, I wish I knew more :X