How does Hamlet plan to test the guilty conscience of Claudius

Hamlet is one of the four pure tragedies of William Shakespeare. Here we see that Hamlet meets the Ghost of his late father. It tells him that his uncle Claudius has murdered his father. Hamlet is very much shocked to have been informed of it. He is determined to take revenge upon Claudius. But before materializing it, he wants to be sure of the fact. So he wants to stage a play containing a scene in which a villain will murder his brother and marry the widow of his dead brother.

According to Hamlet, Claudius' reaction after seeing this scene will reveal whether he is actually a murderer or not. If Claudius is the murderer of the old king, he must be upset to see the play. Hamlet says--

"The play's the thing Wherein I'll catch the conscience of the King."

Hamlet asks Horatio to watch the King's face in the course of the performance of the play, "The Murder of Gonzago" and let him know afterward the conclusion he comes to. In the play scene of "The Murder of Gonzago", Hamlet sits at Ophelia's feet rather than close to the Queen. At first, there is a dumb show. The story of the dumb show closely corresponds to the story told by the Ghost. It shows a loving king making love with his queen. When the queen is asleep, the queen departs. Another man comes and pours poison into the eyes of the sleeping king. The kind dies. Afterward, the man proposes to the queen who almost readily accepts his love. However, the dumb show does not perturb the king. 

After the dumb-show, the actual play is staged. There is a long conversation between the Player King and the Player Queen. The Player King says that after his death the Queen shall have a second husband. But the Queen asserts that she will remain a widow. After the departure of the Player Queen, the King's nephew Lucianus enters and pours poison into the ears of the sleeping King, namely Gonzago. Thus Claudius watches for the second time the staging of his crime. He suspects that the speech of Lucianus is written by Hamlet himself. Claudius rises from his seat, calls for light, and leaves the scene. Observing Claudius' reaction to the play, now Hamlet is sure that he is the murderer of his father. Now he wants to take revenge upon Claudius. 

However, Hamlet thinks that taking revenge for his father's death is his divine duty. But before taking revenge on Claudius, he wants to be sure of the fact. He does not want to rely only on the Ghost's statement. He feels that Ghost may be an evil one. He does not want to act only upon its words without any concrete proof. He arranges to stage a play to catch prey. Thus Hamlet is successful to catch or test the guilty conscience of the King by enacting the play-within-play.