Gertrude tells Claudius that her son is insane and has murdered Polonius. (She doesn't tell him that Hamlet thinks he killed Old Hamlet. Why?)
Claudius thinks this is definitely time to get rid of young Hamlet – he compares the boy to one of those diseases you accidentally spread because your shame won't let you tell anybody you have it.
Gertrude points out that Hamlet is now inspired to cry a little. His madness seems to be letting his morality shine through. In this way, the murder of Polonius has done some good – Hamlet is in touch with his feelings.
Claudius bids Rosencrantz and Guildenstern to go fetch Hamlet, talk to him nicely, and retrieve Polonius's body. Further, they should tell their wisest friends what's been done and what they're going to do about it. All they can do is hope they'll be spared public slander for their involvement in the whole messy affair.