If you're not in a rush and you want to unlock all the Island Sanctuary exclusives with a minimum of effort, this guide is for you.
Part 0: Unlock Island Sanctuary
Before you can unlock Island Sanctuary, you have to complete the final quest of Endwalker (quest title: "Endwalker").
Next, speak to the Clueless Crier near the Old Sharlayan Aetheryte (X:11.9 Y:11.0) to begin the quest "Seeking Sanctuary".
At the Moraby Drydocks in Lower La Noscea, talk to Baldin until you are on the island. Talk to Tataru until the quest is completed.
Part 1: Working toward Automation
Early on, there is some unavoidable effort, but you will eventually be able to automate things on the island.
Build the Cabin
Talk to the Felicitous Furball until the Islekeep's Index appears on the screen. You can now ride a mount, but can't fly yet. Click the flashing icon and choose Gather mode. Click the ⚙️ in the upper-right of the Islekeep's Index and display Vegetation, Trees, and Rocks/Mineral Deposits.
Speed Things Up with Island Sprint
When not riding a mount, you can use the Island Sprint duty action, which has a shorter cooldown than regular Sprint, to be constantly sprinting while you're on the island.
Gather the following:
List of Islekeep's Stone Hatchet Material Sources
2x Stones (from Smooth White Rocks)
3x Palm Leaves (from Palm Trees)
2x Island Branches (from Tualong Trees)
Use the Isle Return duty action, then talk to the Furball. Click the hammer 🔨 icon in the Islekeep's Index to open the Sanctuary Crafting Log, then craft the Stone Hatchet (Your minimum Island EXP afterward: 370).
Where Did the Node Go?
Nodes disappear after you gather from them, but they will reappear after you gather from 11 other nodes. If you can't find the type of node that you need, gather something else first, then go back.
Talk to the Furball until the building site appears. Then gather the following:
List of Cozy Cabin I Material Sources
5x Stones (from Smooth White Rocks)
10x Palm Logs (from Palm Trees - this also gets you the 10x Palm Leaves that you need)
5x Vines (from Island Apple Trees)
5x Sand (from Submerged Sand/Mound of Dirt - choose "Display Soils" to show them on the map)
(Your minimum Island EXP afterward: 620)
Use Isle Return, check on the Cozy Cabin Logboard, and click the Construct button. Check the Logboard again to fully complete the construction. (Your minimum Island EXP afterward: 1370, Your minimum inventory afterward: 5x Apples)
Talk to the Felicitous Furball to complete the Vision. (Your minimum Island EXP afterward: 870, Your minimum Seafarer's Cowries afterward: 500, Your minimum Island Rank afterward: 2, Your minimum inventory afterward: 5xApples)
Don't Spend Seafarer's Cowries at the Cowrie Exchange yet!
The Cowrie Exchange is now available, but don't spend blue Cowries there yet. You will need to spend them on other things to progress. (If you can't resist buying some things from the Cowrie Exchange, just be sure to keep at least 500 Cowries on hand.)
Talk to the Felicitous Furball to start the next Vision.