1) You can start this quest by using the catherby teleport in your spellbook and then walking north until you reach camelot castle. Here you will see a man named "King Arthur".
Talk to him and he will ask if you want to start desert treasure, say yes.
2) He will now give you your first task, you must walk to Ardougne and steal a cake. The only way of going their is by walking.
Follow this map:
You will end up near a stall like this:
Thieve it once and then teleport back to catherby and go to King Arthur again.
3) King Arthur will take the cake from you and give you another task, to get a magic shortbow. Just buy one from from the archery store in falador if you do not already have one and talk to him again.
4) Now it is time for your final task. King Arthur now wants you to fight 4 bosses.
After accepting to fight the bosses you will teleported to the first boss, Dessous. He attacks with melee but does not hit often.
After you have killed Dessous you will be teleported to the next boss, Kamil. He attack with melee and mage. Protect for magic and melee are highly recommended.
After you have killed Kamil you will be teleported to the next boss, Fareed. He attacks with mage. You cannot avoid them by praying, you will just have to constantly eat.
After you have killed Fareed you will be teleported to the next boss, Damis. He attacks with melee, protect from melee is recommended.
After killing Damis you will have finished the quest, congradulations you can now wield ancient staff's!