He was the one who engineered King Hamlet's death by dropping poison in his ear while he was asleep. After the drop of poison was planted, King Hamlet's body was in shock and died seconds later.
Act 1 Scene 2
Claudius is introduced with Laertes, Polonius, Hamlet, Gertrude, Ophelia, and Fortinbras. Claudius, who announces that Prince Fortinbras has not appealed to surrender, dispatches a messenger to advise.
After everyone leaves the Castle Hall, Hamlet mentions how Claudius could have married Gertrude yet a month has not passed.
When the messenger arrives to Fortinbras, the prince explains that there was a misunderstanding; his platoon has battled against uprising monsters to defend themselves. Regardless, he willing stands down to appease Claudius.
Act 1 Scene 4
Hamlet follows his fathers ghost, and the two eventually meet face-to-face. King Hamlet foretells that his brother, Claudius, put poison in his ear, causing his death. King Hamlet demands his son to bring vengeance by killing his brother, to which his son agrees.
Act 2 Scene 2
Claudius greets Rosencrantz and Guildenstern who have arrived in Denmark. The King then requests them to watch over Hamlet.
Act 3 Scene 1
Hamlet, who is under heavy pressure, tries to prove Claudius's guilt with a play "The Murder of Gonzago", which re-enacts how King Hamlet died. Hamlet advises his companions to watch Claudius's expressions.
After "Gonzago" is poisoned and the play ends, Claudius shakes nervously but eventually abruptly arises and leaves. Hamlet sees this as proof of guilt.
Act 3 Scene 2
Claudius has become very disturbed and suspicious of Hamlet since "The Murder of Gonzago". He then dispatches Rosencrantz and Guildenstern to bring Hamlet to England as well as Polonius to spy on Hamlet. Claudius weeps on the floor, fearing for his life.
Oh,
My offence is rank. It smells to heaven.
What form of prayer,
Can serve my turn.
O wretched state! O bosom black as death.
Act 4 Scene 1
Claudius, who fears Hamlet, immediately dispatches Hamlet to England while giving Rosencrantz and Guildenstern a letter, ordering the King of England to immediately kill Hamlet the moment he reads the letter.
Eventually, Hamlet reads the letter, who shakes in anger and despair.
Act 4 Scene 2
Laertes, who has heard the word of Polonius's death, marches back to Denmark with an angry mob. He declares damnation against Claudius for vengeance, and kills all the guards that stand in his way.
When Laertes enters the Castle, he demands his father. Claudius tells him that he was killed by Hamlet. The King devises a plan to achieve Laertes's vengeance.
Claudius learns Ophelia's death from Gertrude, but he says nothing.
Act 4 Scene 3
Claudius walks with Laertes and Gertrude over to Ophelia's grave. When Hamlet appears, Claudius says nothing.
Act 5 Scene 2
Laertes has devised a sparring match with Hamlet using a poisoned sword, which is a part of Claudius's plan. After Laertes cuts Hamlet's cheek, Claudius offers his nephew poisoned wine, who refuses as he wants to finish the sparring match. Gertrude drinks the wine in Hamlet's stead. Claudius, who just noticed his wife attempting to drink the wine, advises her not to, but it is too late for she has already taken a sip. When both Laertes and Gertrude fall, Claudius tries to appease the crowd by saying that the Queen fainted at the sight of the fencers bleeding, but she denies and announces that she has been poisoned.
Laertes then tells that Claudius had designed his blade to be poisoned. Hamlet, enraged, rushes to Claudius and slices him, then forces the poisoned wine down his throat to make sure he dies, finally 'avenging' his parents.