There are six Extra Cases in all, all of which serve to completely refill your stamina. One is in the prologue, two are in Episode 1, and three are in Episode 2. Nothing more needs to be done for the cases; select them, watch the cutscene, get credit.
The prologue should be done just before you head for the bathroom to end the episode and start on the next episode. Episode 1 is fairly long if you take the time to do extra cases, but it's best to break it up as one before the stunt scene activated by talking to Roland Walken, and the other before collecting all the clues on the plane. Episode 2 isn't quite as long. First meal around getting locked into the cargo container, second before opening the door you need to power up, third before inspecting the black jacket.