Final Fantasy XIII-2 showed up earlier than expected and I managed to put about an hour into it last night. I really have no idea what's going on story-wise, but I imagine that everything will be explained eventually. There's a nice recap feature on the main menu to go over the story of FFXIII in order to get you up to speed. It's a similar setup to the recaps in the Yakuza games where it's split up into chunks that you can check out at your liesure. The only difference is that instead of replaying cutscenes, it's got a little video that plays, while a narrator recaps each chapter of the first game.
They drop you into the action pretty quickly. So far the battle system seems about the same. I'm switching paradigms like a pro. I don't think I'm able to make my own paradigms, or switch around their order yet.
The enemies seem to pop up somewhat randomly, but you have this guage that shows up around you. It gives you a visual representation of how far, and which direction you need to run to avoid the fight, and how much time you have initiate a pre-emptive strike.
Again, I'm only one hour into a 30 hour game, so I can't do a whole lot yet.