Quick answer: Complete the Rescuing the Crew quest first, then sail to the second island, locate all three shipwrecks, and repair the one in the middle of the island using 100 Wood, 20 Nails, 20 Coarse Fabric, and 10 Ropes. After repairing it, return to the first island and speak with Doctor Galen to finish the quest.

Prerequisites before starting the quest
The I Need a Bigger Boat quest becomes available in the Windrose demo shortly after you wrap up the initial tutorial. Before you head out to find shipwrecks, though, you need to finish the Rescuing the Crew quest. The game won't let you repair a ship without a crew to do the work, so skipping this step will leave you stuck at the wreck with no way to proceed.
You should also make sure you have a solid stockpile of resources before sailing to the second island. Gathering materials on the second island is possible, but the area is crawling with hostile enemies, and running back and forth to farm Wood or craft Nails while dodging patrols is not a great time.

Sailing to the second island safely
Once you've rescued your crew, use your starter boat to sail to the second island. If you've somehow lost track of your small vessel, press K on your keyboard to summon it directly to your position near the water. This is a lifesaver if you die on the second island and respawn back at your base — you don't need to start over or reload a save.
All three shipwreck locations
There are three wrecked ships scattered across the second island. You need to discover all three before the game lets you begin repairs, but only one of them actually needs to be fixed.
The first wreck sits on the north-west shore of the second island. When you interact with it, the game tells you it's beyond repair. This one is essentially a dead end, but you still need to examine it to progress the quest.

The second wreck — and the one you'll actually repair — is located in the middle of the second island. This area is heavily guarded by enemies patrolling around the ship. Try to pull individual enemies away from the group rather than fighting them all at once. Windrose's combat punishes recklessness, and getting swarmed near the wreck is a common way to lose progress.
The third wreck is elsewhere on the island and will be marked on your map once you've found the first two. You need to visit it to "discover" it, but you don't have to repair this one.
To make tracking easier, open your menu and set the I Need a Bigger Boat quest as your active tracked quest. This places markers on your map showing the repairable ship locations so you aren't wandering the island blind.

Repair materials for the ship
Interacting with the repairable wreck in the middle of the island reveals the exact resource requirements. You'll need all four of these in your inventory before you can start the repair.
| Material | Quantity |
|---|---|
| Wood | 100 |
| Nails | 20 |
| Coarse Fabric | 20 |
| Ropes | 10 |
Wood is the easiest to gather — just chop trees on either island. Nails, Coarse Fabric, and Ropes all require crafting at your base workstations. Make sure your Smelting Furnace and other crafting stations are built and operational before you attempt this quest, since you'll need them to process raw materials into the finished components.
If you've been following the Islander tutorial questline and building up your base camp, you should already have most of these resources or the means to produce them by the time you reach this point in the demo.

Completing the repair and finishing the quest
Step 1: With all four materials in your inventory and your crew rescued, walk up to the repairable shipwreck in the center of the second island and interact with it. The repair will consume the materials and trigger a completion sequence.
Step 2: After the ship is repaired, sail back to the first island. Find Doctor Galen and speak with him. He'll tell you about recovering an artifact from the prologue, which wraps up the I Need a Bigger Boat quest entirely.
Once the conversation with Doctor Galen ends, the quest completes, and you unlock the Seafarer tutorial. This opens up the naval side of Windrose, giving you access to a larger ship capable of actual sea combat and longer voyages across the archipelago.

What to do if you lose your boat during the quest
A common frustration during this quest is dying on the second island and losing access to your raft. If you respawn on the first island with no boat in sight, don't panic and don't restart your save. Simply press K to summon your starter boat back to you. This works from anywhere and instantly brings the small vessel to the nearest water.
The larger ship you repair during this quest operates on a different system. Later in the demo, if that ship gets destroyed in naval combat or sails out of bounds, you can rebuild it at a Wharf structure at your base for just 20 Wood. The Wharf becomes available after you complete the cannon-crafting quest that follows the Seafarer tutorial.
The I Need a Bigger Boat quest is one of the first major progression gates in the Windrose demo, and it sets the stage for everything that comes after. Once you have your larger ship and the Seafarer tutorial unlocked, the game shifts from pure island survival into open-water exploration and ship-to-ship combat, which is where Windrose really starts to open up.