Traditionally, Act 2 of a Shakespearean play provides the rising action and the complications to the plot elements established in Act 1. In this play, Act 1 establishes the current state of Denmark and specifically, Hamlet's state of mind. He is mourning the death of his father, King Hamlet, and is disgusted by his mother's remarriage to his Uncle Claudius. The act ends with his conversation with the ghost of his dead father who reveals he was actually murdered by Claudius and now wants Hamlet to avenge his death.
Act 2 adds complications in that Hamlet has decided to "put an antic disposition on" in the hopes that Claudius might do something in an unguarded moment that would reveal his guilt. The theme of appearances and acting builds here: Hamlet appears to be crazy; Claudius appears to be a concerned father who is worried about his "muched too changed son;" Polonius appears to be a confident adviser to the king when he claims to know the cause of Hamlet's lunacy; Rosencrantz and Guildenstern want to appear as good friends of Hamlet, but are actually serving as spies for the king and queen. There are also actual actors who have arrived and are going to put on a play which Hamlet plans to change slightly in the hopes that with the play he can "catch the conscience of the king."
Another key theme of the act is the theme of loyalty. Polonius shows loyalty to the king and queen by revealing what he thinks he knows about Hamlet's crazy behavior -- stemming from the lost love of his daughter Ophelia. Hamlet test Rosencrantz and Guildenstern's loyaly when he asks "whether you were sent for or no" and they reveal their lack of loyalty when they lie to him over and over. Hamlet reveals that he knows he can't trust them. Ophelia is loyal to her father as evidenced by the fact that she agrees to go along with the plan to talk with Hamlet while her father and Claudius are spying.
This brings up a third theme: spying. Polonius hires a man named Reynaldo to go and spy on Laertes to see how he is behaving while away at school. Rosencrantz and Guildenstern are brought to Elsinore to spy on Hamlet. Hamlet is acting crazy as a way to spy on Claudius. Polonius sets up another spy session. Hamlet plans to use a performance of the play as a means to spy on Claudius and observe his reactions.