When you first enter this area, you need to get the ornimental key.
Advance down the sole path, there's a werepanter and other enemies in the way. You should reach some down stairs, with an archer overlooking the area. If you want the mystic urn, jump on the side railing, and use that to leap towards the doorway frame. This extends two steps you can use to reach the urn.
In the first square room, step on the two floor switches to open the side passages. Take the passage on the left. Although it leads to a dead end, there is a door that opens in place of one of the torch alcoves. Ahead is a metal railing, but advancing will smash bits of the railing away. To avoid this trap, simply drop down to the platform below the entrance, handle the archer, and use the teleporter. This places you near the oriental key, and you can simply walk or run back the way you came without having to worry too much about the jumping puzzle.
For now, you've done everything here, return to the Plaza of the Sun. You can continue here when you have the jade and crystal skulls.
Unlocking the map
When you return here with the two skulls, you can head to where there was previously two floor switches. This room has three exits, two of which require the jade and crystal skulls. Using these
The last exit on the map (leading to the bridge of stars) is just before the skull room, but you need all four elements for that region to be useful.