The URL for this is:

FF7 Advent Children Page

Here's the translation that I came up with:

Girl: The life of the Planet, Lifestream. On that day, to protect itself, the Planet used its power, because it wanted to go on living. But on that day, many people died. On that day, many souls died. Now there's nothing to believe in.

Cloud: I think I want to be forgiven. Yes, I want to be forgiven.
...
Cloud: I'll live for your sake as well. I've decided.

It may be a little inaccurate (but there's only one line where I had to look a word up), but it should give you a good idea of what's going on.

This trailer has some footage from the ending of the game FF7, which is pretty cool. It's awesome that the graphics look pretty good even today. Enjoy!