When you enter, take the two nearby Djose Spheres - one at a time, of course - and put them into the door to the north. Shock-ingly enough, it’ll open! Your task is to light up the Yevon symbol on the floor.
Beyond, you’ll see two spheres, one each on the oblique walls nearby. Take each and put them into the two slots on the east side of the area; the ceiling will glow after, so push the pedestal underneath the glowing pillar. This, in turn, will give a charge to the Djose Sphere on the pedestal. Take this charged Sphere and place it into the slot of the northeast-oblique wall, just east of the northern door. Said door should open.
Now, go to the east side, where those two Djose Spheres are. Snatch each and put them on the pedestral, then go to the west side of the room and step on the glowing tile to reset the pedestal. Push the pedestal into the room to the north, then into the electrically-charged gap: the electromagnetism in the gap will hold the pedestal in place due to the Djose Spheres, making a viable way across. Simply jump on it, then push the pedestal northward on the other side of the gap. Doing so will end up revealing part of the main Djose glyph in the previous room.
Go back to that room and step on the glowing tile to the west to again regain your pedestal. Take the super-charged Djose Sphere that opened the room to the north, then place it on the wall to the west to reveal more of the Yevon symbol. Take each of the Djose Spheres from the pedestal now and place them into the slots on the east and west wall of the first room of the Cloister. This will complete the symbol, making an elevator. Get on it, a la Mushroom Rock, to ascend.
In this area, go north and you’ll find five pedestals. As logic would suggest, simply push each backward into the wall to complete some more electrical circuits. Go downstairs now and you’ll see a glyph on the wall to the far west (it’s whitish-grayish, not green): examine it to find a Destruction Sphere . Take it back upstairs to the newly-formed pedestal and place the Destruction Sphere atop it to find a Magic Sphere chest. After, go west and upstairs; the Cloister is done!