Giving unsolicited advice seems to be a character trait of the people in Polonius's family. In act 1, scene 3 of Shakespeare's Hamlet, Laertes is preparing to board a ship to France, which is the context in which much of the advice-giving occurs between and among Polonius, Laertes, and Ophelia.

Before Polonius gives advice to Laertes about how to conduct himself in France, Laertes first gives advice to Ophelia about her relationship with Hamlet, then Ophelia gives advice to Laertes about practicing what he preaches. This exchange of advice between Laertes and Ophelia might have continued for several more lines, except that Polonius enters the scene and interrupts their conversation.

When Polonius enters the scene, he urges Laertes to be on his way to the ship bound for France.

POLONIUS. Yet here, Laertes? Aboard, aboard, for shame!
The wind sits in the shoulder of your sail
And you are stay'd for.
(act 1, scene 3, lines 58–61)

Then, while the captain, crew, and all of the passengers on the ship wait for Laertes to come aboard, Polonius takes several minutes to give advice to Laertes, which is probably the same advice that Polonius gave to Laertes the previous time, or times, that Laertes went to France—or at any time that Laertes goes anywhere else, for that matter.

Polonius's advice to Laertes is so clear and direct, and so well-known, that little of what Polonius says needs further explanation.

POLONIUS. And these few precepts in thy memory
See thou character.
(act 1, scene 3, lines 62–63)

This is an odd line to the modern eye, and especially to the modern ear, particularly when "character" is pronounced with the emphasis on the second syllable. This conforms to the iambic pentameter of the line, but it gives the word the sense of being a verb, rather than a noun.

Scholars differ about the interpretation of the line. Some scholars assert that the line means that Laertes should remember what Polonius says and apply it to his character, and others contend that "character" refers to writing down Polonius's advice. Both schools of thought agree, however, that Polonius is telling Laertes to remember what he tells him, even though Laertes likely has already committed it to memory, having heard the same speech many times before.

POLONIUS. Costly thy habit as thy purse can buy,
But not express'd in fancy; rich, not gaudy;
For the apparel oft proclaims the man,
And they in France of the best rank and station
Are of a most select and generous, chief in that.
(act 1, scene 3, lines 74–77)

Polonius's advice about clothing seems like something with which Polonius might not concern himself. The only other time that clothing is mentioned in the play is when Hamlet's mother tells him to "cast thy nighted color off" (act 1, scene 2) for constantly wearing black clothes around the castle, and Hamlet defends his choice of "inky cloak" and "customary suits of solemn black" as "but the trappings and the suits of woe."

Here, Polonius is saying, "Buy the best clothes you can afford but nothing too fancy, because, as they say, 'the clothes make the man.'" Keeping in mind that Laertes is going to France, specifically to Paris—apparently a fashion center at the time, as it is now—Polonius wants Laertes to remember that the upper classes and nobility will judge him by his clothes.

One of Polonius's most famous maxims, "Neither a borrower nor a lender be," occurs later in his lengthy lecture, followed a few lines later by the equally famous, "This above all: to thine own self be true" (act 1, scene 3).

Notable about Polonius's advice to Laertes, particularly in the context of Laertes and Polonius's advice to Ophelia about Hamlet in the same scene and considering the fact that Laertes is going to the "big city" of Paris, is that Polonius gives Laertes no advice whatsoever about his interactions and relationships with women.

Polonius talks about nothing else with Ophelia, but he doesn't say a word about it to Laertes. Once Laertes exits the scene, for instance, Polonius can't resist asking Ophelia about her relationship with Hamlet, and he then gives her advice about how to behave with him.

Even though Laertes goes to Paris, which is more than twelve hundred miles away from Elsinore Castle, Polonius isn't done giving advice to him. In act 2, scene 1, Polonius send his servant, Reynaldo, to Paris with "this money and these notes," which "notes" no doubt contain additional advice for Laertes.

Polonius also gives Reynaldo detailed instructions and advice on how to spy on Laertes, which is Polonius's primary reason for sending Reynaldo to Paris with the money and notes for Laertes. Polonius simply can't help himself. He's obsessed with giving advice to anyone and everyone, from his servant to the king and queen of Denmark.

In the dialogue between Polonius and Reynaldo in act 2, scene 1, there's a subtle clue about why Polonius gives so much advice to Laertes about returning to France. Polonius cautions Reynaldo about asking too many questions and probing too deeply into Laertes's behavior.

POLONIUS. You must not put another scandal on him,
That he is open to incontinency.
(act 2, scene 1, lines 31–32)

This "scandal" might be the reason that Ophelia tells Laertes to consider his own behavior when he gives her advice about her relationship with Hamlet.

OPHELIA. Do not, as some ungracious pastors do,
Show me the steep and thorny way to heaven,
Whilst, like a puff'd and reckless libertine,
Himself the primrose path of dalliance treads
And recks not his own rede.
(act 1, scene 3, lines 50–54)

Ophelia's reference to a "reckless libertine" is intriguing, particularly since Polonius makes no mention of anything even remotely related to Laertes's behavior with women in his advice to him in act 1, scene 3.

Either Polonius doesn't know about his son's behavior in France, which seems unlikely, since Polonius later mentions Laertes's "scandal" to Reynaldo, or Polonius simply doesn't know what to say to him—which never stopped Polonius from giving advice to anyone before—or Polonius subscribes to the patriarchal precept of a male-dominated society that "boys will be boys."

In Act 1, Scene 3 of Hamlet, Laertes is about to embark for France to attend the university. His father Polonius gives him the following famous lines of advice.

Give thy thoughts no tongue,
Nor any unproportion'd thought his act.
Be thou familiar, but by no means vulgar.
Those friends thou hast, and their adoption tried,
Grapple them to thy soul with hoops of steel;
But do not dull thy palm with entertainment
Of each new-hatch'd, unfledged comrade. Beware
Of entrance to a quarrel; but being in,
Bear't that the opposed may beware of thee.
Give every man thy ear, but few thy voice;
Take each man's censure, but reserve thy judgment.
Costly thy habit as thy purse can buy,
But not express'd in fancy; rich, not gaudy;
For the apparel oft proclaims the man,
And they in France of the best rank and station
Are of a most select and generous, chief in that.
Neither a borrower nor a lender be;
For loan oft loses both itself and friend,
And borrowing dulls the edge of husbandry.
This above all: to thine own self be true,
And it must follow, as the night the day,
Thou canst not then be false to any man.

Although Prince Hamlet regards Polonius with contempt, and although the old man does seem foolish on more than one occasion, his advice to his son is full of sound practical wisdom. No doubt this wisdom is coming from Shakespeare himself and he is only using Polonius as his spokesman. For instance, Shakespeare twice cautions young people to be very careful about what they say to others.

Give thy thoughts no tongue

And:

Give every man thy ear, but few thy voice

What Shakespeare's character Polonius says about borrowing or lending money is also good advice, as many people can attest from experience.

Neither a borrower nor a lender be;
For loan oft loses both itself and friend,
And borrowing dulls the edge of husbandry.

What Polonius means by borrowing dulling the edge of husbandry is that if you get into the habit of living on borrowed money you can dig yourself into a hole that will be hard to climb out of. Borrowing also tends to make a person careless about earning, saving, spending, and budgeting. 

The best advice of all comes last and is the hardest to follow:

This above all, to thine own self be true

It is hard to follow because it is hard to understand your own self. But it is worth the effort to do so. If you understand yourself you will make better career decisions, a better marital choice, better friends, and end up leading a more satisfying and prosperous life. Robert Frost wrote about making a choice between two diverging roads in his famous poem "The Road Not Taken." He made his decision based on his knowledge of himself. There are many times in life when we have to decide something for ourselves and no one can advise us. We come to a lot of diverging roads, or what William James called "crossroads situations," in life. Polonius says, "Take each man's censure, but reserve thy judgment." By "censure" he means advice. A lot of people will offer you free advice, and you should listen to them--but in the end you should make your own decisions.

Buddha is quoted as having told a disciple:

Do not believe anything anybody tells you, including anything I tell you, unless it agrees with your own experience and your own common sense.

In Hamlet, Act 1 scene 3, Laertes is getting ready to go to France. He warns his sister, Ophelia, to not to become in love with Hamlet. Laertes cares deeply for his family and worries about his sister getting hurt by Hamlet. As he is getting ready to leave his father comes in to offer some advice to his son before he sets off to France. His advice is fatherly advice because he wants the best for his children.

Yet here, Laertes! aboard, aboard, for shame!
The wind sits in the shoulder of your sail,
And you are stay'd for. There; my blessing with thee!
And these few precepts in thy memory
See thou character. Give thy thoughts no tongue,
Nor any unaproportioned thought his act.
Be thou familiar, but by no means vulgar.
Those friends thou hast, and their adoption tried,
Grapple them to thy soul with hoops of steel;
But do not dull thy palm with entertainment
Of each new hatch'd, unfledged comrade. Beware
Of entrance to a quarrel, but being in,
Bear't that the opposed may beware of thee.
Give every man thy ear, but few thy voice;
Take each man's censure, but reserve thy judgement.
Costly thy habit as thy pursue can buy,
But not express'd in fancy; rich, not gaudy;
For the apparel oft proclaims the man.
And they in France of the best rank and station
Are of a most select and generous chief in that.
Neither a borrower nor a lender be;
For loan oft loses both itself and friend,
And borrowing dulls the edge of husbandry,
This above all: to thine own self be true.
And it must follow, as the night the day,
Thou canst no then be false to any man.
Farewell! my blessing season this in thee!

Laertes is seen to be the complete opposite of Hamlet. If only Hamlet had a father who had given him this same kind of advice, how would the tale had ended?
 

As Laertes is leaving for France in Act 1, Scene 3, Polonius tells him to be careful about what he says. He also tells Laertes to keep his trusted friends close. Polonius continues with different bits of advice which include avoiding quarrels, reserving judgment, and dressing with sophistication (in France). Polonius closes his comments to Laertes with the more famous lines: "Neither a borrower nor a lender be, / For loan oft loses both itself and friend, / And borrowing dulls the edge of husbandry." (I.iii.75-77) 

Polonius' last bit of advice is perhaps more central to the play: 

This above all--to thine own self be true,

And it must follow, as the night the day,

Thou canst not then be false to any man. (I.iii.78-80)

Laertes heeds this advice. When he returns to Denmark, he plans to avenge his father. Laertes is tricked by Claudius into conspiring against Hamlet but Laertes never hides his true feelings, one of the characters in the play that really doesn't act falsely. Claudius and Hamlet, on the other hand, are constantly conspiring and hiding their true feelings.