For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
Jim Hawkins is a boy working at his parents' inn when a drunken old sailor comes to stay. This sailor, Billy Bones, has a treasure map leading to the buried hoard of fearsome pirate Captain Flint. Once Jim finds the map in Billy's sea chest, he brings it to the local judge, Doctor Livesey. Doctor Livesey and his friend, Squire Trelawney, hatch a scheme to go on a treasure hunt. The three set out from Bristol on the Hispaniola with a crew largely hired by helpful, gentlemanly sea-cook Long John Silver. Of course, this crew is a crew of pirates who just want to use the Hispaniola to get them to Captain Flint's island. But Jim and his friends don't know that – at least not at first.
Act II
The second act is the part of the story where everything seems as far as possible from a conclusion. When Jim overhears Long John Silver's plans to mutiny once the Hispaniola arrives at Treasure Island, he runs and tells Doctor Livesey, Captain Smollett, and Squire Trelawney. At this point, the good guys are outnumbered. Once they reach Treasure Island, through a series of ambushes and surprise attacks, the good guys manage to whittle the number of pirates down to a handful by the time Jim becomes a pirate hostage. Now the pirates' numbers are low, they are struggling among themselves, and the good guys have taken control of the Hispaniola. But we still don't know where the treasure is, the key point of conflict for both sides.
Act III
This is the moment when everything gets solved. In Chapters 33 and 34 we finally discover what has happened to Captain Flint's gold. As long as the pirates can keep hoping for treasure, all of their problems (sickness, losing the Hispaniola, and failing confidence in their elected captain, Long John Silver) seem manageable. But once Tom Morgan, George Merry, and Dick Johnson find that the treasure has already been dug up, they totally lose control. They rush to attack Long John Silver without realizing that the good guys – Doctor Livesey, Abraham Gray, and Ben Gunn – have been following them on their trek across the island. Just at this moment, Doctor Livesey and the rest come out of the forest, attack the remaining pirates, and rescue Jim and his unusual ally, Long John Silver. The remaining pirates flee and the good guys get away from the island with a fortune in gold bars.