How do you save on la noire

The game saves automatically and incrementally, there is no save function. However, there is a load function and an alternate "Cases" menu where you can repeat any case that you have completed before if you wanted to better your rank or attempt a different conclusion path (some cases have alternate endings and some have different paths to the same ending).

If you wanted to do something different during a case, you can quit the game at any time and when you continue, it will do so from your last case checkpoint (eg, as you arrive at a new location, just before questioning a suspect, at the beginning of a foot or car chase, etc.). If you wanted to go before that checkpoint, you will have to restart the case, but not the rank.