As you are in the 1st pyramid where you initially started there is a passage with a block which has an eye-smbol on it. The block moves as soon as you approach it so you can't pass it. Make yourself invisible with Taklit's part to overcome it.
You will reach a tomb with skeletons and some snakes in it. The wall on the rear side of the central structure can be crumbled with Urgon's part. Inside you can climb up.
Up there you'll reach a room with a "flying-man" symbol on the floor. This is a hint that you'll eventually use Azerim's part to fly up from here. However, this is not possible yet because there is a closed grate in the way which must be opened first.
Make sure you cleared the room from any creature. Especially look down into the hole, there is probably a spider waiting.
Now proceed upstairs. You'll reach some kind of trap door. Make a quicksave before you try to get over it, you must be really fast.
Above that trap door you'll find a button. This will open the grate in the room below, but only for a short time. So you have to press this button and then run as hell until you're back to the room below. There you can float up using Azerim's part - but only if you were fast enough.
The way down is different from the way you came from. Take the elevator, it's around the next corner. It's not easy at all because the grate opens just for a very little period of time, but after some tries you'll make it.
Finally, after floating up you'll find yourself near the last fireplace.