The Corsair Curse/Quick guide

The cursed crew

 * Speak to Captain Tock just south of the Falador chicken farm. (Chat 2-1)
 * Board the ship south of The Rusty Anchor pub (right-click the gangplank during the short cutscene, and select "Cross" when the cutscene is over to automatically walk there.)
 * Speak to Captain Tock again. (Chat 1)
 * Speak to either Arsen the Thief, Cabin Boy Colin, and Gnocci the Cook, upstairs on the buildings directly west of the platform. (Chat 1)
 * Speak to Ithoi the Navigator, who is found south west of the platform, on a small portion of stairs, next to the water.. (Chat 1)
 * You can do the next three sections in any order.

Arsen's, Colin's and Gnocci's "curse"

 * Speak to Arsen the Thief. (Chat 1)
 * Speak to Cabin Boy Colin. (Chat 1)
 * Speak to Gnocci the Cook. (Chat 1)
 * Grab the tinderbox next to him if you don't have one.
 * Grab the spade found directly South of his hut (Tropical tree near shore) if you don't have one.
 * Receive the ogre artefact from Captain Tock. (Chat 1)
 * Speak to Ithoi the Navigator
 * Use the telescope in Ithoi the Navigator's hut.
 * Dig by the lump of sand next to the tree where Gnocci the Cook fished in the cutscene.
 * Three steps East of the Tropical tree found West of the fishing spot
 * Enter the dungeon to the North and slightly east and speak to Chief Tess in the dungeon to the northwest. (Chat 1)
 * Return and speak to Arsen the Thief, Cabin Boy Colin, and Gnocci the Cook

Traitor in the Midst

 * Speak to Captain Tock. (Chat 1-1)
 * Speak to Gnocci the Cook. (Chat 1)
 * Speak to Arsen the Thief. (Chat 1-1)
 * Speak to Ithoi the Navigator. (Chat 1-1)
 * Speak to Ithoi the Navigator again. (Chat 1-1)
 * Light the driftwood under his hut using the tinderbox.
 * Speak to Captain Tock. (Chat 1-3)
 * Kill Ithoi the Navigator(level 32)
 * Speak to Captain Tock. (Chat 1)

Congratulations, quest complete!