What final plans are arranged in Act 4, Scene 7 of "Hamlet"?
Simply put, Claudius receives a letter half-way through the scene that Hamlet is to return to Denmark. Agreeing with Laertes (Hamlet, remember, has killed Laertes' father, Polonius) that Laertes should be the one to kill Hamlet, Claudius devises a plot to murder Hamlet. Here's the summary he makes of it at the end of the scene:
When in your motion you are hot and dry—
As make your bouts more violent to that end—
And that he calls for drink, I'll have prepared him
A chalice for the nonce, whereon but sipping,
If he by chance escape your venom'd stuck
Our purpose may hold there.
Laertes and Hamlet will fight in a fencing match: when the two become "hot and dry" (throated!), Hamlet will call for a drink. Claudius will have prepared a poisoned chalice for Hamlet to murder him: that is, if the poison on the point of Laertes' sword does not kill him first.
Well, the King guides Laertes into planning a cunning revenge on Hamlet (he says, so, that really stinks that Hamlet killed your Dad...whatcha going to do about it, huh?). Laertes decides (with the King's help) that he'll challenge Hamlet to a sword-fight, lace his sword-tip with poison and stab him! The King says, yes, yes, this is excellent, and just in case THAT doesn't work, I'll have a cup of poison for him to drink out of. All of this sets the scene for the cataclysmic ending where the entire royal family is wiped out at the end of the play-classic Shakespeare. :)