In Shakespeare's Hamlet, you may remember that at the start of the play (I.iii), when Laertes is departing for school, Laertes (and Polonius) warns Ophelia about Hamlet and his attentions toward her. Laertes tells her that he will use her, take her virginity, but never marry her because he must serve the state and marry someone appropriate to his position of prince, but will forget Ophelia. So we know at the start that Laertes does not have an overly favorable regard of Hamlet—specifically in terms of Ophelia's relationship with him.
In Act Five, scene one, Laertes has returned to news of his father's death at Hamlet's hands. (As a note, now Hamlet, Laertes and Fortinbras have lost their father.)
This is the scene in the cemetery, where Hamlet speaks the famous line about the court jester during his youth, whose skull he holds:
Alas, poor Yorick! I knew him,
Horatio... (lines 172-173)
As Horatio and Hamlet speak, Hamlet realizes that there is a burial taking place nearby, looking as if the death had been a suicide ("maimed rites"). Laertes is there, speaking, and Hamlet makes note of it: speaking admiringly of him.
That is Laertes, a very noble youth. (line 217)
As they listen, Laertes asks that more be added to the funeral service, perhaps a mass. The priest refuses, stating that "she" is lucky to be buried in holy ground at all—and only by the order of the King. Laertes goes into the grave to embrace his sister once more, and then Hamlet, realizing the body is that of Ophelia, does the same, noting that he also is devastated by her death.
Laertes springs to attack Hamlet, cursing him:
The devil take thy soul! (line 257)
Hamlet tries to remove Laertes' hands from around his neck, warning Laertes of danger if he continues:
I prithee, take thy fingers from my throat;
For, though I am not splenitive and rash, (260)
Yet have I in me something dangerous,
Which let thy wisdom fear. Hold off thy hand!
The two young men need to be separated. Hamlet swears to continue to fight, and Gertrude asks Hamlet why.
I loved Ophelia. Forty thousand brothers (270)
Could not, with all their quantity of love,
Make up my sum.
Hamlet then asks Laertes what is wrong with him, to attack Hamlet. Hamlet admits that he has loved Laertes always, bearing him no grudge:
Hear you, sir!
What is the reason that you use me thus?
I loved you ever. (lines 291-293)
Hamlet is then led away by Horatio.
In Act Four, scene seven, Claudius spoke to Laertes about punishing Hamlet for Polonius' death. At the end of this scene, Claudius reminds Laertes of that discussion. In this way, we know that Laertes is committed to murdering Hamlet, with the King's blessing.
Strengthen your patience in our last night's speech.
We'll put the matter to the present push.— (lines 297-298)
Hamlet did kill Polonius, but it was accidental. He also has no way to know that Claudius is plotting with Laertes, though he will understand it clearly enough when the "sword play" is announced between the two men. Laertes' rage with Hamlet puzzles him here, but it will make more sense when the competition between the two men is arranged, for Hamlet will then suspect "knavery." Laertes has expressed his willingness to kill Hamlet—even in a church (Act Four, scene seven), so it is safe to assume that where Hamlet is confused about Laertes hatred for him, Laertes is committed to the purpose of ending Hamlet's life.