How does Laertes behave when he returns to Elsinore after his father's death in Shakespeare's Hamlet?

From the moment Laertes returns to Elsinore in Act IV, Scene 4, he is a man of action. When we last saw him, he was preparing to leave for school. Then, he was a practical and politically astute man. He warned Ophelia to “fear” the fact that, as a prince, Hamlet’s wife would be the result of political expediency, not love (I.3.16-33). He patiently endured a rambling (second) farewell from his father, then took his leave with dignity and grace.

Compare that figure, then, to the man who storms into Elsinore in Act IV. Laertes is now leading a rebellion upon the castle:

[Y]oung Laertes, in riotous head,
O’bears your officers. The rabble call him Lord...
They cry, "Choose we! Laertes shall be king!" 
                                                     IV.4.104-10

When Laertes barges into the throne room and finds Claudius, there is no sense of loyalty or political decorum. He calls Claudius “vile king” and forcibly demands answers from him.

Laertes is enraged over his father’s mysterious death and “obscure funeral" (213), where Polonius received no political honors or rites. It seems Laertes will stop at nothing to get answers. Only Ophelia’s madness gives him momentary pause, but Claudius manages to stoke Laertes’s wrath once more and focus it on a new target: Hamlet. That done, we once again see the change Laertes has undergone since Act I as he swears he would go so far as to “cut [Hamlet’s] throat i’ the church” (IV.6.122).

From there, Laertes is just different shades of vengeful grief: jumping into his sister’s grave, getting into a fistfight with Hamlet over her body, and concocting a plot to poison the prince.

But the honorable and conscientious Laertes of Act I is not completely gone. Before striking Hamlet with the poisoned sword tip, he tells us killing Hamlet now is “almost against [his] conscience” (V.2.290). When Laertes is poisoned, his Act I self comes to the fore once more. He confesses his sin to Hamlet and points the finger at the master culprit: “The king! The king’s to blame!” (314)

All of this action is precipitated by the unjust murder of Laertes’s father. For deeper insight into the play, consider how Laertes’s actions differ from Hamlet's, who is also motivated by a father’s murder. It tells us much about the difference between these two men—and why Shakespeare chose to write a play called Hamlet and not one called Laertes.