Enter Hamlet, Rosencrantz, and Guildenstern:
This short scene opens with Hamlet's words, "Safely stowed" (4.2.1), indicating that he has just hidden Polonius' body, although we never do learn why he hides the body. He seems to have no intention of pretending that he didn't kill Polonius. Perhaps he's just acting crazy.
Rosencrantz and Guildenstern are hot on Hamlet's trail, and we can hear them shouting "Hamlet! Lord Hamlet!" Soon enough, they appear and ask Hamlet what he's done with the body of Polonius. They tell him that they want to take the body to the chapel. Hamlet replies, "Do not believe it," and when Rosencrantz asks "Believe what?" Hamlet answers, "That I can keep your counsel and not mine own" (4.2.11). This is a little obscure. "To keep counsel" means to keep a secret, so Hamlet is saying that they shouldn't think that he can keep their secret, but not his secret. His secret is where he has hidden Polonius, but what's their secret?
After this, Hamlet directs a stream of insults at Rosencrantz. He tells Rosencrantz that he is a "sponge," and that although he's now soaking up the King's favors, when the King is done with him, he'll squeeze him dry. Rosencrantz replies that he doesn't understand, but he's probably lying, because Hamlet's message is quite clear. Hamlet has been insulting Rosencrantz and Guildenstern ever since he found out that they were working for the King, and Rosencrantz probably figures it's just better to let all that stuff roll off his back.
At any rate, Rosencrantz gets back to the point, telling Hamlet, "My lord, you must tell us where the body is, and go with us to the king." Hamlet answers with some "mad" talk, saying, "The body is with the king, but the king is not with the body. The king is a thing--" (4.1.27-28). (This is part of legal doctrine. "The body is with the king" means that the king, in his own body, can enforce the king's laws; "but the king is not with the body" means that you can't stop obeying the king's laws when the king is dead, because the king is not just a body, but a principle.) Hamlet hasn't finished his thought, probably to lure a response out of his two "friends." Guildenstern bites, saying "A thing, my lord?" Hamlet delivers the punch line, "Of nothing," meaning both that the king is an idea, a no-thing, and that this particular king, Claudius, is a good-for-nothing, and will soon be--if Hamlet has his way--nothing but a dead body.
Finally, Hamlet appears to calm down, saying "bring me to him," but he's just fooling. He suddenly turns and runs, saying "Hide fox, and all after," as if they were children playing hide-and-seek. Rosencrantz and Guildenstern run after him, and the scene's over.