Instructions
Accept the Desert Treasure quest chain in the Bedabin Camp. You will be given a task to obtain four diamonds from different locations in RuneScape's world. Go to the road north of East Ardougne and encounter Raslo the merchant, walking along the path. He will sell you the Ring of Visibility. Once you get the ring, you can put the Desert Treasure quest on hold in order to get the Ghostly Robes first.
Go to Lumbridge Swamp and complete Father Uhrney's quest, which awards you the Ghostspeak Amulet. Equip the amulet and ring in order to see and speak to ghosts, which are the only requirements for this mini-quest.
Travel to Glarial's Tomb, which is northwest of the fishing guild. Here, look for a transparent human named Valdez. Talk to him and he will award you the Ghostly Top. Then ask that you find another ghost named Rennard. Valdez will tell you to go to the Pirates' Hideout, the Bandit Camp in the wilderness or the Bandit Camp in the Kharidian Desert. Depending on the location Valdez gives you, you will receive a different set of directions from Rennard, leading you to the four other ghosts with the complete set. Find each of these ghosts to complete the Ghostly Robes set.