Quote 1
POLONIUS
He knew me not at first; he said I
was a fishmonger. He is far gone. And truly, in my
youth, I suffered much extremity for love, very near
this. (2.2.205-208)
Polonius is convinced that Hamlet is "far gone, far gone" in his love for Ophelia. But—sorry, Polonius—we think it's more likely that Hamlet is likely making a naughty joke at Polonius' expense: a "fishmonger" is slang for "pimp." I.e., Hamlet knows that Polonius is basically pimping out his daughter to get at Hamlet.
Quote 2
POLONIUS
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.
(1.3.84-86)
Polonius likes to dish advice, but he sure can't take it. Given Polonius' penchant for spying on his children and Hamlet in order to curry favor with King Claudius, he's not in any position to be talking about truth.
Quote 3
POLONIUS
Marry, sir, here's my drift,
And I believe it is a fetch of wit.
You laying these slight sullies on my son,
As 'twere a thing a little soiled i' th' working,
Mark you, your party in converse, him you would
sound,
Having ever seen in the prenominate crimes
The youth you breathe of guilty, be assured
He closes with you in this consequence:
'Good sir,' or so, or 'friend,' or 'gentleman,'
According to the phrase or the addition
Of man and country—
(2.1.43-54)
What was that about honesty, again? Here, Polonius instructs his servant to spread rumors about his son Laertes in the hopes of finding out what the boy's up to. Obviously, this way of thinking has some major flaws—but this is actually pretty much the same method Hamlet uses to find out whether or not the ghost is telling the truth about Claudius. Hm.
Quote 4
POLONIUS
At such a time I'll loose my daughter to him.
[To the King.] Be you and I behind an arras then.
Mark the encounter:
(2.2.176-178)
Oh, look, it's Polonius again. Here, he's colluding with the King to deceive Hamlet—and it ends up getting him killed. We can't feel too sorry.
Quote 5
POLONIUS
Ay, springes to catch woodcocks. I do know,
When the blood burns, how prodigal the soul
Lends the tongue vows. These blazes, daughter,
Giving more light than heat, extinct in both
Even in their promise, as it is a-making,
You must not take for fire. From this time
Be somewhat scanter of your maiden presence.
(1.3.124-130)
Ophelia's virginity is a family affair: her dad agrees with her brother that her sexuality makes her vulnerable to damage. But it also makes her powerful: in Polonius' hands, Ophelia is nothing more than a tool to reveal Hamlet's state of mind.
LORD POLONIUS
[…]From this time
Be somewhat scanter of your maiden presence.
Set your entreatments at a higher rate
Than a command to parley. For Lord Hamlet,
Believe so much in him, that he is young,
And with a larger tether may he walk
Than may be given you. In few, Ophelia,
Do not believe his vows, for they are brokers,
Not of that dye which their investments show,
But mere implorators of unholy suits,
Breathing like sanctified and pious bawds
The better to beguile. This is for all:
I would not, in plain terms, from this time forth
Have you so slander any moment leisure
As to give words or talk with the Lord Hamlet.
Look to 't, I charge you. Come your ways.
OPHELIA
I shall obey, my lord.
(1.3.129-145)
After a lengthy speech about why Ophelia can't trust anything Hamlet says or promises (including any and all "vows" of love), Polonius orders Ophelia to stop seeing Hamlet. As an unmarried daughter, Ophelia has no choice but to "obey," and she does. We soon learn that Ophelia rejects all of Hamlet's letters and refuses to see him—until she gets used as bait to spy on Hamlet. Essentially, Ophelia is powerless —over her own body, over her relationships, over her activities, and even over her speech. It's no wonder that she cracks.
POLONIUS
[…]
I would not, in plain terms, from this time forth
Have you so slander any moment leisure
As to give words or talk with the Lord Hamlet.
Look to 't, I charge you. Come your ways.OPHELIA
I shall obey, my lord.
(1.3.141-145)
Ophelia isn't actually agreeing here; she's just acknowledging that she has to obey Polonius. Parents in this play (and in powerful families of the Early Modern period) weren't necessarily interested in helping their kids develop to their fullest potential, or whatever the helicopter parenting line is now; they saw their kids as pawns in the game of life.
Quote 8
POLONIUS
[…] and there put on him
What forgeries you please—marry, none so rank
As may dishonor him, take heed of that,
But, sir, such wanton, wild and usual slips
As are companions noted and most known
To youth and liberty.
(2.1.21-26)
In a long tradition of helicopter parenting, Polonius spies on his kid while he's away at college. And he's not the only one. Claudius, Hamlet's step-father / uncle, also goes to great lengths to find out what Hamlet's up to and even tries to have him murdered. We know that Hamlet idealizes his own father, but we wonder —if Old Hamlet were still alive, would he be any better than Claudius and Polonius?