I don't know about you, but I personally have not played Final Fantasy VII in I-don't-know-how-many years; and even when I had played it I never ended up finishing it. And from everything I've heard, you have to be familiar with the storyline of the game in order to enjoy (or at least understand) the Advent Children movie.
So with that in mind, I scoured the net in a desperate attempt to find some kind of re-cap material from the game. I ended up having some success, so I thought I'd share it here for all you who might be in a similiar situation. So here you go:
First off, here's a list of the characters from the game who are supposedly going to be in the movie.
The Final Fantasy Shrine is a pretty comprehensive respository of need-to-know FF7 info.
If you own the game and just want to get through it quickly to experience the story, you can always to this quick walk-through.
And last but not least, here's some Wikipedia info on the seperate but related Last order anime, which may or may not be on the Advent Children DVD. Plus, as an added bonus, here a quasi-legal bittorrent link.