The Act opens with Lord Polonius instructing his servant, Reynaldo, to spy on his son Laertes, who has left for Paris. Polonius gives Reynaldo very specific instructions as to how he has to go about tracing Laertes and finding out exactly what he has been up to.
The purpose of opening the Act with this scene is to emphasize Polonius' duplicitous nature. It also supports the theme of treachery. By spying on Laertes, Polonius betrays his son's trust. He had advised Laertes before he undertook his journey about his conduct and what his expectations as a father were. Laertes promised that he would heed Polonius' advice, but his father seems to doubt his integrity and therefore deems it appropriate to spy on him.
The scene further illustrates how sly and conniving Polonius can be. He specifically instructs Reynaldo to blatantly lie about what he knows of Laertes and go on a "fishing expedition", as it were. Reynaldo is to claim that he only knows Laertes as a hazy acquaintance but that Laertes possesses certain identifiable qualities. All of these would be obvious lies. Reynaldo's listener/s might then feel it incumbent on himself/themselves to provide further information about Laertes. He would thus have craftily gleaned information about Laertes and would then report to Polonius.
Polonius' cunning is clearly illustrated when he says to Reynaldo:
"Your bait of falsehood takes this carp of truth:
And thus do we of wisdom and of reach,
With windlasses and with assays of bias,
By indirections find directions out:"
Polonius is clearly a doting, overprotective father who has the tendency to meddle in his children's affairs. He obviously does not trust them and believes that what he does is in their best interest. This is proven when he questions Ophelia about her acquaintance with Hamlet and advises her to stay away from him. He admits that he is a jealous father when he tells Ophelia:
"I fear'd he did but trifle,
And meant to wreck thee; but, beshrew my jealousy!"
This happens when she later informs him about Hamlet's reaction after she had followed his advice and rejected Hamlet's advances.
It is this meddlesome attitude that gets Polonius killed later. He hides behind a curtain in Lady Gertrude's chambers to snoop on Hamlet. When Gertrude screams, thinking Hamlet is about to kill her, Polonius cries out from behind the arras and gets stabbed, by Hamlet, through the curtain. Polonius dies.
This tragic incident spawns greater tragedy later.
This opening scene of Act II furthers the concept of spying and surveillance evident throughout the play. It also presents the idea of Hamlet as "madly in love", with 'mad' here meaning insanity.
As the act opens, Polonius is instructing Reynaldo to go and essentially spy on his son Laertes. He gives him several tips, including to ask his companions of their impressions of Laertes, and to bribe people if necessary. This parallels the advice he's given to Laertes and Ophelia earlier in the play. It also introduces a duplicitous nature to Polonius' character. Sure, he's a daffy fool, but here he's also a scheming parent who lacks trust in his child.
After Reynaldo leaves, Ophelia reveals Hamlet's strange behaviour to her father. Polonius decides Hamlet's actions are based on his obsessive love for Ophelia. Polonius has no evidence on which to base this conclusion, but of course he doesn't let that stop him. This belief leads to tragic consequences for himself and his children.