Oh boy, that one is a pain. Basically, you have to match the shapes on the screens to the shapes activated by the panels on the floor.
I used a pen and paper to jot down a map; that kind of helped. You could try making a diagram showing each panel, with a number to show the correct sequence you've got to activate them in. In the large chamber, with the circular opening in the floor, you have to activate panels that correspond to matching shapes. Make a pair of identical shapes, then the next pair, and so on.
There's probably a more specific guide in the FFX section of Gamefaqs.com.