In Act 1, Scene 2:
* He urges Claudius to be patient and understand Hamlet's grief for his father. He suggests that Hamlet's melancholy is due to his father's death and that time will heal his sorrow.
* He proposes spying on Hamlet. He suspects Hamlet's madness is connected to his love for Ophelia and suggests having Ophelia play the role of a conduit to get information from him.
In Act 2, Scene 2:
* He reports to Claudius and Gertrude about his observations of Hamlet. He claims that Hamlet is "mad for love" and that he has discovered the root cause of his distress.
* He reveals the contents of Hamlet's letter to Ophelia. He uses this to further reinforce his claim that Hamlet's love for Ophelia is the source of his madness.
* He proposes that they arrange for Hamlet to be secretly observed. He believes this will allow them to determine the true nature of Hamlet's madness.
In Act 3, Scene 1:
* He instructs Ophelia to be polite but reserved when interacting with Hamlet. He tells her to avoid making any accusations or judgments about his behavior.
* He warns Ophelia that Hamlet's "love" may not be genuine. He fears that Hamlet is merely using Ophelia as a pawn in his own game of madness.
Overall, Polonius's advice and actions are driven by a desire to maintain order and control. He is often more concerned with his own reputation and status than with the well-being of others. His attempts to manipulate and spy on Hamlet have ultimately tragic consequences, leading to his own death in Act 3, Scene 4.