There are two views to this speech to Laertes ( Hamlet, I,iii). The first is an obvious comparison with Hamlet. His father is dead and cannot give Hamlet advice, except as a ghost, while Laertes has his father still alive (at least for a few more scenes). If taken literally, the advice is standard father-son talk, a little pompous (“Neither a borrower nor a lender be”) and not carefully listened to. A far more interesting view is that Polonius is giving advice that Shakespeare finds hypocritical and falsely felt, that the speech is to be heard by the audience (and reader) as the opposite of “good advice.” Is “To thine own self be true” really good advice (some critics amend the ending: “Thou canst then be false to any man”); and is Polonius really a “good father” or has he clustered all his fathering in this one “sage advice” to his already grown son? Polonius as a character is a sort of sycophant to the new court, and his relationship to Claudius seems self-serving rather than genuine. What was his relationship to Hamlet’s father? Few clues are available. The actor playing the role must choose a tone that is either genuine or pompous. If you factor in two other pieces of information from the play— that he is also Ophelia’s father and that his accidental death at Hamlet’s sword is hardly mourned except by Laertes—you can see how both interpretations could be supported—wisdom and irony.
That he should stick to his studies. Have fun, but not too much fun. And not to get into fights.