This will be either your first or second trophy in the game. It is unmissable as it is part of the main story.
Once you enter the cloister do the following:
1). Examine the Glyph on the wall. This opens up a new path. Another Glyph appears on the right side. Examine it to reveal a secret chamber.
2) Descend the stairs and view a short tutorial. Obtain the Glyph sphere and insert it into the door at the bottom of the stairs. Once the door is open take the sphere back.
3) Go to the next sphere recess and insert the Glyph sphere. You will open a chamber containing the Destruction sphere. Don't get it yet.
4) Examine the runes across from the pedestal to reveal a Glyph. Touch it and it reveals a chamber containing the Besaid sphere. Take it.
5) Insert the Besaid sphere into the nearby pedestal and it opens up another chamber. Leave it for now and return to the Destruction sphere.
6) Place the Destruction sphere in the same slot you first found the Besaid sphere. This opens a hidden chamber on the far side of the Cloister containing a treasure (Rod of Wisdom)
7. Finally return to the pedestal and push it into the slot on the floor. This concludes your first Cloister of Trials puzzle.