Francisco and Marcellus have called Hamlets friend Horatio to show him a monster that has been lurking in the castle. He is being escorted by Bernardo, a fellow guard himself.
"A monster! A monster in the form of the late King Hamlet! We must inform Hamlet immediately, he must visit his fathers ghost. Only he can bring this ghost to peace. Only he can listen."
"Listen Hamlet my son, I was killed by a snake, but, the snake that did sting thy fathers life now wears his crown. An ear full of poison is what killed me!" Hamlet tries to make sense of this. His own uncle killing his father to take his thrown. He must get revenge!
During the coronation of his uncle, Hamlet is still thinking about his father and is plotting revenge. His uncle Claudius tells him to stop thinking about his father and move on. He then goes on to call Hamlet his son. This frustrates Hamlet!
Hamlet tells a group of local actors about a play he wishes to make for the king. He insists that the last scene be when the king is murdered by his uncle. Poison is to be dropped into his ear. Hamlets plan is to recreate his fathers death in front of Claudius and observe his reaction. Hamlet is excited about the play.
During the last scene Claudius becomes severely distressed and runs out of the play after screaming for it to stop. This is more than enough proof for Hamlet. Claudius killed King Hamlet!