Saving your progress in Phantom Hourglass is straightforward but has a unique mechanic tied to the Spirit Train. You cannot save at any point you wish in the overworld or dungeons. Instead, you must return to your ship, the S.S. Linebeck, or find a specific save point. The primary method for saving is to interact with the Diary located in Linebeck's cabin on the S.S. Linebeck. Simply tap on the diary, and you'll be prompted to save your game. It's crucial to save frequently, especially before entering new dungeons or after completing significant objectives, as unexpected game overs can set you back considerably.
Additionally, there are Mailboxes scattered across various islands. Interacting with a Mailbox will also give you the option to save your game. These are less common than returning to your ship but serve as convenient save points when you're exploring an island extensively. Always keep an eye out for these red boxes. Remember, if you get a Game Over, you will restart from your last save point, so make it a habit to save after every major accomplishment or before attempting a challenging area. Losing progress can be frustrating, so prioritize saving!