Progress through the Dungeon and Village until you get to the Wastelands. Go through these until you get to the Tower, approach it and enter it. This is RNG, but eventually you'll get an option for Library. This part is all RNG related, but you want to Search until you get the Diary.
Note: if you get the books Cookbook and Adventure book, make sure to read these as well to get progress towards the Reader achievement. Please see that for more information.
Upon getting the Diary, select these options:
Observe three times in a row