which character opens scene 2? what is he expalining to the court?

What act are you referring to?

Scene 2 is a masterful production put on by the new king, Claudius. It is very calculating and it stands in contrast to the appearance of the ghost in the prior scene. Claudius is an actor playing the part of a king, a role to which he has no right. He is a murderer and a usurper. But now he stands on his stage in the spotlight to tell the court and the people of Denmark that all is well and under his control. Of course the scene as a whole is tightly controlled by Claudius. His language is balanced to the point of being oxymoronic. First, he addresses the circumstance of sadness in the death of King Hamlet yet joy in marriage to the sister queen. He moves quickly to address the urget matters of state. That pesky upstart Prince Fortinbras is deftly handled diplomatically. Only then does Claudius turn to a personal matter of his most trusted counsellor, Polonius. Laertes is given permission to leave the country and head back to school in France. The final act of this little play by Claudius is to put Hamlet in his place. Of course Claudius has already primed his audience; Claudius present himself as a knowledgeable and reasonable individual. Hamlet is truculent and ill suited for the task Claudius has seized upon. Hamlet comes off as anything but kingly. After Claudius leaves Hamlet a throughly whipped school boy, he exits the stage with a flourish along with the rest of the court dutifully following. Claudus is a dude who has his act together.