The Witch Islands can only be found once you have researched the Winch and Throwing Rings technologies, which are unlocked as Phase 7 of Research.
You will need the following materials for both items’ research:
Iron Bars x4: obtained by refining Scrap Metal at the Smelter.
Forcers x2: made at the Workbench, each one requires 1 Iron Bar and 1 Grease. You get Grease by refining Fat and Chemicals at a Lab.
Bolts x2: made at a Workbench, each one requires 1 Iron Bar.
Complete the research and craft the items, which will require you to get the materials again. You might also want to craft more than one set of Throwing Rings, just to be safe.
Once you’ve completed the research, the islands will start appearing. They can be found along the train’s path, usually marked by a series of fireflies near debris.
Fireflies are small white flying bugs that fly in clusters. If you see them near debris, they’re leading you toward one of the Witch Islands!
Use your newly obtained Throwing Rings and Winch to grapple onto the debris and follow the fireflies. The fog will obscure your vision, but just keep following the clusters of fireflies.
You will eventually notice sets of structures in the distance, such as trees and houses. That’s the Witch Island, so just continue making your way toward it!
Congrats, you should’ve made your way to one of the Witch Islands now! Solve their puzzles to get rewarded with a chest containing many helpful resources.