Two primary scenes regarding deception in Act II have to do with Polonius and Laertes, and with Hamlet's old school chums Rosenkrantz and Guildenstern. Both situations involve spying and lies in different ways.
Polonius, at court in Elsinore with the increasingly erratic Hamlet and his worried daughter Ophelia, feels that he could use some support from his son, Laertes. He is concerned that Laertes's distance from Denmark is distracting him from the importance of the events in his homeland. Wanting to find out whether he can count on his son, Polonius decides to circulate false reports and see who, if anyone, endorses or repeats them.
Claudius has also become concerned about Hamlet's behavior, and he is not fully convinced that his nephew is as deranged as he seems. The larger question of Hamlet's feigning madness or having truly gone off the rails is an underlying theme of the play. In this act, Claudius's plan starts to be exposed. He brings two of Hamlet's former classmates to court to get reacquainted with him in the hopes that Hamlet will be forthright with them, or if not, that they can figure out whether he is faking. Their charge is to deceive their old "friend," pretending they want to catch up for old times' sake while they really report back to Claudius behind Hamlet's back. Later, this idea spectacularly backfires when Hamlet deceives them and the authorities, and gets Rosenkrantz and Guildenstern killed.
Hamlet himself goes in and out of the action, and seems determined to convince all the others that he is mad—thus better advancing his own investigations and scheme of revenge against the usurper Claudius.