Start by talking to the broken clay golem outside of the ruins of Uzer. Ask if you should repair it. Use your clay on the golem to repair it. When it is whole, it will tell you its task is incomplete, and that you should open the portal for it to kill the great demon.
Pick the nearby letter up from the ground and read it. Then, go down the stairs into the ruins. Take the strange implement from the northwest corner, then pick some black mushrooms from the northeast.
Opening the Portal
Head to the northeastern area of the digsite and look for Elissa.
Tell her you found the letter, and she will tell you his notes are in the exam centre to the south. Search the bookcase in the southeast corner to find his notes. Read (or skim) through the book to find out a lot of things, firstly bein that the Varrock museum has the missing statute.
Head to the Varrock Museum and talk to the Curator. He won't let you have the key, so pickpocket him. Go up the stairs. The northwestern most display has the statute. Right click to open it. With the statute, and head back to the desert. First, instead of going to Uzer right away, head to the mine to the northwest of Uzer.
Look for the desert phoenix and try to grab a feather from it. Now, back in the ruins of Uzer, go in the middle of the room, and place the statute on the alcove. Turn all the statutes so they're facing towards the center of the door on the south end.
When you have it right, they will be locked in place. Enter the door to enter the demon's throne room. You will see its skeleton lying on the floor nearby. Optionally, with a chisel and hammer, go to the north end of the room and use it on the throne to receive gems.
Try talking to the Golem, but it won't listen. Use a pestle and mortar on the black mushroom to get ink. Use the phoenix feather on the ink to get a quill pen. Then, use the quill pen on the papyrus to write instructions.
Use the strange implement on the golem. Then use the golem program on it. It will update its program.