In the Restore the… Outdoor Bookshelf you have to first find some missing items (9 Board Pins and 5 Shingle Tiles) to restore the Outdoor Bookshelf (Orders Board).
Open the quest and click “Start Quest” so you can start picking up Shingle Tiles you may have noticed lying around your farm.
To get the Board Pins, just plant and harvest crops as usual.
When the parts start showing up, click on them.
After you find all the missing items, install them by clicking on the “outdoor bookshelf” or the quest menu.