The Corsair Curse/Quick guide

The cursed crew

 * Speak to Captain Tock. (Chat 2-1)
 * Board the ship south of The Rusty Anchor pub.
 * Speak to Captain Tock again. (Chat 1)
 * Speak to Arsen the Thief, Cabin Boy Colin, and Gnocci the Cook. (Chat 1)
 * Speak to Ithoi the Navigator. (Chat 1)
 * You can do the next part in any order.

Arsen's "curse"

 * Speak to Arsen the Thief. (Chat 1)
 * Receive the ogre artefact from Captain Tock. (Chat 1)
 * Speak to Chief Tess. (Chat 1)
 * Return to Arsen the Thief.

Colin's "curse"

 * Speak to Cabin Boy Colin. (Chat 1)
 * Use the telescope in Ithoi the Navigator's hut.
 * Return to Cabin Boy Colin.

Gnocci's "curse"

 * Speak to Gnocci the Cook. (Chat 1)
 * Dig by the lump of sand next to the tree where he fished in the cutscene.
 * Return to 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)
 * 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.
 * Speak to Captain Tock. (Chat 1)

Congratulations, quest complete!