Early in the story, you'll meet a character named Tallow. Interact with Tallow, then select the "I want to donate something to your cabinet" option. This will open your backpack and allow you to choose the items that you want to donate to Tallow's collection.

You can donate a variety of items that you discover on the island to Tallow's collection, such as resources, critters, and fish. Tallow also provides rewards when a new item is added to their collection.

Items you have yet to donate will have "New! Donate to collections for a reward" in their description if you select them while in your backpack or storage.

You will need to have the item you want to donate in your backpack when you talk to Tallow. If there's nothing for you to donate, the option in her menu will say, "I have nothing to donate, but let me check".