'Everybody's Gone to the Rapture' features an autosave system. There is no manual save option. The game saves automatically at frequent intervals, typically after you've triggered a significant narrative event, entered a new area, or interacted with a key object. You'll see a small icon appear on the screen to indicate a save is in progress.
While the autosave is generally reliable, it's always a good idea to finish a narrative sequence or reach a new distinct location before quitting the game, just to ensure your progress is fully recorded. You can safely exit the game from the pause menu at any time, and upon reloading, you will typically resume from the last autosave point.