So this is the scene in which Polonius and his children give each other lots of advice. Really, that's about all that happens here, other than establishing that Hamlet's been professing to love Ophelia. Did this start before or after his father's death? I kind of think before, but certainly it's been a fairly recent development, since Polonius seems only peripherally aware of it. Either that or they've been keeping it a secret really well.
When talking about Hamlet choosing a bride, Laertes says, "on his choice depends The safety and health of this whole state," (19-20) and he's saying something wiser than he knows, isn't he? The health and safety of Denmark and especially its heads of state depend on Hamlet's choices of what to do with the information he'll receive from the Ghost.
I always get a kick out of Polonius' idea of what "few" means. His "few precepts" for Laertes to remember run on for 22 lines.
"I shall the effect of this good lesson keep
As watchman to my heart" (44-45).
"Those friends thou has, and their adoption tried,
Grapple them unto thy soul with hoops of steel" (61-62).
"Give every man thy ear but few thy voice" (67).
"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" (77-79).
Possible Discussion Questions:
A lot of times, Polonius gets portrayed as very abrupt and terse toward Ophelia, but I think you can also read this section as him being very caring and concerned for her welfare. The same goes for his interaction with Laertes -- Polonius may be a tedious old windbag, but he gives good advice. I think his "to thine own self be true" (77) gets quoted at least as much as "To be or not to be." What do you think? Is he concerned about their welfare, or only about how their behavior reflects on himself?