
Enter HAMLET, reading
LORD POLONIUS: O, give me leave:
How does my good Lord Hamlet?
HAMLET: Well, God-a-mercy.
LORD POLONIUS: Do you know me, my lord?
HAMLET: Excellent well; you are a fishmonger.
Famously, a "fishmonger" is a colloquial term for a pimp (a rather rude one when you think about the etymology). Either Hamlet knows that Polonius aims to use his daughter against him, or irony is at work. It also lends support to the idea that Hamlet has bedded Ophelia, as do many other sexually suggestive lines throughout the play.
LORD POLONIUS: Not I, my lord.
HAMLET: Then I would you were so honest a man.
LORD POLONIUS: Honest, my lord!
HAMLET: Ay, sir; to be honest, as this world goes, is to be
one man picked out of ten thousand.
The play is very much interested in the idea that everyone is an actor. Here, Hamlet acts the fool and Polonius patronizes him, both ironically searching for the truth, but neither showing their true selves. As in the "beauty/honesty" exchange that comes later, Hamlet here says that he'd rather Polonius admit he is a "fishmonger" than keep up pretenses. Avowed criminals are at least honest in that they do not pretend to be innocent.
LORD POLONIUS: That's very true, my lord.
HAMLET: For if the sun breed maggots in a dead dog, being a god kissing carrion,--Have you a daughter?
LORD POLONIUS: I have, my lord.
HAMLET: Let her not walk i' the sun: conception is a
blessing: but not as your daughter may conceive.
Friend, look to 't.
Hamlet again suggest that he has had his way with Ophelia, though naysayers can justify it as simple cruelty towards her father. The potential pun between "sun" and "son", however, may indicate more. Hamlet creates a disturbing image in which he compares children to maggots and women (Ophelia? Gertrude?) to carrion (a dead dog, specifically). There is a streak of self-loathing in this even if Hamlet may sarcastically be comparing himself to the sun and a god. If Gertrude is the carrion, then he is a maggot. If Ophelia, then he is the breeder of maggots and warns Polonius against himself. In the broader picture, what is "bred" in Elsinore is decay. Hamlet warns that everyone's actions are leading to tragedy, including his own. Of course, Polonius doesn't get it.
LORD POLONIUS: [Aside] How say you by that? Still harping on my daughter: yet he knew me not at first; he said I was a fishmonger: he is far gone, far gone: and truly in my youth I suffered much extremity for love; very near this. I'll speak to him again. --What do you read, my lord?
It's the first we hear of Ophelia's mother (possibly), and an actor could use it as justification for why Polonius is so adamant that Hamlet's madness stems from deflected love.
HAMLET: Words, words, words.
The first crucial repetition.
LORD POLONIUS: What is the matter, my lord?
HAMLET: Between who?
LORD POLONIUS: I mean, the matter that you read, my lord.
HAMLET: Slanders, sir: for the satirical rogue says here that old men have grey beards, that their faces are wrinkled, their eyes purging thick amber and plum-tree gum and that they have a plentiful lack of wit, together with most weak hams: all which, sir, though I most powerfully and potently believe, yet I hold it not honesty to have it thus set down, for yourself, sir, should be old as I am, if like a crab you could go backward.
Hamlet plays more than the fool in this scene, he plays the Fool. This character present in both Greek and Elizabethan drama acts the clown, but tells the truth, usually escaping punishment for the latter thanks to the former. In this sequence, we have Hamlet doing just that (though he is safe for other reasons). He tells Polonius exactly what he thinks, but the veil of madness means he may not be taken seriously. As the scene continues, Hamlet even prophesies his own death:
LORD POLONIUS: [Aside] Though this be madness, yet there is method in 't. --Will you walk out of the air, my lord?
HAMLET: Into my grave.
LORD POLONIUS: Indeed, that is out o' the air.
[Aside] How pregnant sometimes his replies are! a happiness that often madness hits on, which reason and sanity could not so prosperously be delivered of. I will leave him, and suddenly contrive the means of meeting between him and my daughter.--My honourable lord, I will most humbly take my leave of you.
The mention of pregnancy has not fallen on deaf ears. Shakespeare, through Hamlet, has just underlined the power of words, after all.
HAMLET: You cannot, sir, take from me any thing that I will more willingly part withal: except my life, except my life, except my life.
The second crucial repetition and one that is indeed more "pregnant" than the first. Plus, it's preceded by an excellent barb.
LORD POLONIUS: Fare you well, my lord.
HAMLET: These tedious old fools!
At the very end, Hamlet may be letting go of the pretense, commenting on the exchange, though if Polonius is still present (and in the text, he is), it's one more "mad" sting shot in his direction. But as Hamlet's attitude changes in the next sequence (with Rosencrantz & Guildenstern), we must assume he was putting on a show in this one.