Johnny Got His Gun is going to have a bit of an unconventional structure for this kind of plot analysis, because there are multiple ways of determining what the central "conflict" of the story is. Is the conflict Joe trying to reconcile the fact of his lost limbs and senses? Is it Joe trying to communicate with the outside world? Either one is valid. We at Shmoop have decided to use the more external conflict (Joe trying to get the nurse and doctor to understand him), but that doesn't mean that this is the only way to map out three acts in this book. We'll explain our reasoning below.
Act I lasts from the beginning of the novel until Joe decides that he needs to start measuring time at the beginning of Book II. Yeah, that's a big first act. The reason we chose it is because most of Book I is stage setting. We get to know Joe pretty intimately, but nothing "happens," in terms of plot, except that Joe discovers his physical mutilation. His initial revelation could also mark the end of Act I, as both are points of no return; but even after he realizes how badly injured he is, nothing really changes until Book II.
The end of Act II, in which there's been a lot of struggling to cope the reality of being catastrophically mutilated, ends when Joe's at his lowest, when the doctor doses Joe with morphine for the first time and he has that crazy vision of the train. This is Joe's lowest point because things start to look up afterwards, when he gets a new nurse.
The rest of the book constitutes Act III. Here, we recover a bit from the downer of the morphine episode: the new nurse who gives us some hope, and Joe seems to be on the brink of making it all worth it, at least in a way, when… tragedy strikes. Yet again.