Stardew Valley: How To Complete The Museum
Early into Stardew Valley, Gunther from the Museum will come to you with a request. He tells you that the Museum is lacking when it comes to real artifacts and asks you to donate any rare items you find to him. The Museum functions similar to one in the Animal Crossing games, where you need to donate one of each item to complete the collection. Completing the entire collection will earn you a Stardrop, which permanently increases your max energy.
How the museum works
The Museum is open from 8am to 6pm, except during town festivals. It is located in the southeast corner of town, next to the Blacksmith. Inside is a large collection of books, which is where you can read any lost books you find, and a large display area, where new donations go. To donate an item, speak with Gunther and he will let you place any new donations wherever you want, with the option to move them later.
Gunther will also give rewards at certain milestones, including once you donate a total number of certain items, and individual paths for both Artifacts and Minerals. Most of the rewards are nice bonuses, but unimportant, with three exceptions. At 60 items you get the key to the sewers, at 95 items you get a Stardrop, and if you donate all four Dwarvish Scrolls, you get the Dwarvish Translation Guide, which allows you to communicate with Dwarves.