In act 2, scene 2 of Shakespeare's Hamlet, it's not until very near the end of this very long scene that Hamlet's intentions regarding the troupe of travelling players (actors) becomes clear. It's entirely possible that it doesn't even become clear to Hamlet until very near the end of the scene how he intends to make use of the players.

The scene itself is full of conspiracies, so it only seems appropriate that Hamlet should fashion one of his own. The scene opens with Claudius and Gertrude conspiring with Rosencrantz and Guildenstern to spy on Hamlet, to "glean ... what afflicts him." Later in the scene it becomes apparent that Rosencrantz and Guildenstern really aren't very good at spying on Hamlet, who sees through their feeble, transparent attempts to "glean ... what afflicts him" and turns the tables on them, which Hamlet does again in act 3, scene 1.

In this scene Claudius and Gertrude also conspire with Polonius to have Claudius and Polonius spy on Hamlet from "behind an arras" while he talks with Ophelia. This spying occurs later in the play, in act 3, scene 1.

The troupe of travelling players arrives, and after Hamlet has the lead actor perform a lengthy monologue from a play about Dido and Ǽneas for him, Hamlet conspires with him—although the actor doesn't actually know that he's conspiring with Hamlet—to perform a play at court entitled The Murder of Gonzago, into which Hamlet asks if he can insert "some dozen or sixteen lines" of his own devising.

In the last twenty lines of the scene, Hamlet explains his reasoning for this. At some time in his life Hamlet heard that people watching a play have sometimes been so moved by a scene that they feel guilty about something they've done and "proclaim their malefactions." Hamlet thinks that this might work to cause Claudius to confess the murder of Hamlet's father, which will confirm what his father's ghost told him and give Hamlet the proof he needs to take his revenge on Claudius for the murder.

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

This is one of the most famous scenes in Hamlet. In it, Hamlet expresses the oft-quoted line "the play's the thing," which is often repeated without the second half of the sentence: "Wherein I'll catch the conscience of the king." In these lines, Hamlet is explaining what use he is making of the players here and why.

Essentially, Hamlet has devised a plan to have the actors "play something like the murder of [his] father" in front of his uncle, Claudius. He believes that by having the players perform something analogous to the murder of old King Hamlet, he will be able to determine by Claudius's reactions whether he truly is guilty of having killed King Hamlet. To this end, Hamlet calls the actors to him and asks them to perform The Murder of Gonzago, in which a king is killed by poison. While the actors are performing, Hamlet and his friend Horatio pay close attention to the behavior of Claudius; at first Claudius does not seem particularly interested in the play, noting that it is "long," but the play has been specifically chosen by Hamlet because it so closely parallels, in his mind, what has happened to his own father.

Hamlet is not willing to entertain argument on this subject: he feels that if he should see Claudius "blench," or go white, it will be an indication that he is indeed deserving of death, and Hamlet will know what course to take. The implication is of course that he will kill his uncle.

In a soliloquy, Hamlet explains his plan:

I'll have these players
Play something like the murder of my father
Before mine uncle. I'll observe his looks.
I'll tent him to the quick. If he do blench,
I know my course.
(act 2, scene 2, lines 623–627)

In other words, he is tasking the acting troupe with performing a play that enacts a scene very similar to his own father's murder. A ghost resembling Hamlet's dead father, old King Hamlet, has accused his own brother, the current king, Claudius, of murdering the king while he slept in the orchard. The ghost of old King Hamlet claims that Claudius murdered him by pouring poison into his ear. Hamlet plans to observe his uncle, Claudius, as the play is being performed, as he believes that his uncle's behavior will reveal whether or not he is truly guilty of this heinous act of betrayal. Ultimately, in the lines above, Hamlet declares that he will know what to do if his uncle shows signs of guilt.

Hamlet is aware that it might not be his own father's ghost at all but, rather, a "devil" who has assumed a "pleasing shape" in order to trick him and get him to kill the king. For this reason, he says, he wants to be really sure that Claudius is guilty. He finishes his soliloquy with the following famous lines:

The play's the thing
Wherein I'll catch the conscience of the King.
(act 2, scene 2, lines 633–634)

He believes that watching his uncle's response to the play will reveal whether or not Claudius feels the weight of a guilty conscience.

At the end of act 2, scene 2, Hamlet describes how he plans on using the actors to confirm that Claudius murdered his father. When the group of actors arrive, Hamlet plans for them to perform the play The Murder of Gonzago in front of King Claudius and Gertrude in the hopes that the king will reveal his guilt. In act 3, scene 2, the actors perform the "mousetrap" scene, in which they recreate King Hamlet's murder in the orchard. While the actors are recreating King Hamlet's murder, Hamlet and Horatio closely watch Claudius's reaction to the events on stage in order to determine whether or not he displays signs of guilt. As soon as Claudius watches the actor pour poison into the king's ear on stage, he gets up and leaves the theater. Claudius's reaction confirms that he killed Hamlet's father. Unfortunately, Hamlet continues to hesitate and does not act upon his emotions until it is too late.

Hamlet sees an opportunity with the arrival of the players.  He plans for the players to enact The Murder of Gonzago with a few changes/additions. The play will mimic what the ghost has told Hamlet happened to him at the hands of Claudius.  Hamlet plans to watch Claudius for his reaction during the performance of the play. Should Claudius watch the play with little reaction, he will believe the ghost is an evil spirit hoping to damn his soul.  However, if Claudius reacts strangely to the play, Hamlet will take it as proof that the ghost tells the truth and will feel more justified in pursuing action against Claudius.