In Shakespeare's Hamlet, how does Claudius finally die?

Claudius dies shortly after Laertes's fatal duel with Hamlet. Laertes has dipped his sword in poison and grazes Hamlet with it. Hamlet then uses this sword to kill Laertes, who, as he is dying, admits to Hamlet that Claudius is trying to kill Hamlet with poisoned wine. Laertes also admits that his sword has been dipped in poison. When Hamlet hears this confession, he runs the sword through Claudius, saying, "The point envenomed too!—Then, venom, to thy work" (V.2.317-318). This means that he wants the venom or poison on the sword to do its work to kill Claudius quickly. Hamlet also forces Claudius to drink the poison that Gertrude drank (and that killed her) and says, " Here, thou incestuous, murderous, damnèd Dane, Drink off this potion. Is thy union here? Follow my mother" (V.2.320-322). The "union" refers to the pearl that Claudius had placed in Hamlet's cup. Hamlet's means of killing Claudius therefore include a sword hit, poison from the sword tip, and the poison wine.