Act 1 scene 5: Hamlet sees the ghost of his dead father, and knows now that he didn't die in war, something else must have happened
Act 2 scene 2: Hamlet runs into the actors for the play and asks them to change the play by adding in "The Murder of Gonzago" They are confused but do as he says
Act 3 scene 1: Gertrude and Claudius discuss Hamlet and his behavior and Polonius tells Ophelia to return her things to Hamlet while Polonius hides behind a curtain and eavesdrops on their conversation.
Act 4 scene 4: Hamlet is talking with Gertrude and thought that claudius was behind the curtain in the bedroom, but turns out it was Polonius instead. And now he is dead
Act 5 scene 3: King claudius talks to Guildenstern and Rosencrantz about Hamlet and his plan to exile Hamlet. Hamlet already knows this and has a plan of his own.