In Hamlet, how had Laertes found out about Polonius' death?
It appears from the text that Laertes was in France when he heard about Polonius's death, presumably from a friend, acquaintance, or court gossip. Shakespeare doesn't show this scene; it's part of the action that happens offstage.
Our first confirmation that Laertes knows about his father's death comes in Act IV, Scene 5, when Claudius is speaking to Gertrude about Ophelia's psychologically disturbed behavior:
Her brother is in secret come from France;
Feeds on his wonder, keeps himself in clouds,
And wants not buzzers to infect his ear
With pestilent speeches of his father's death;
Wherein necessity, of matter beggar'd,
Will nothing stick our person to arraign
In ear and ear.
The secret nature of Laertes's return from France is consistent with the idea that he learned about the death while he was there, and came back secretly so he could take Claudius—the presumed killer—by surprise.
Note that "wants not buzzers" means Laertes has no shortage of gossip regarding the circumstances of his father's death. He's hearing all sorts of bad things ("pestilent speeches") about it, and Claudius assumes Laertes believes Claudius is responsible.
Later, in Act IV, Scene 5, Laertes rushes into the palace to confront Claudius:
How came he dead? I’ll not be juggled with.
To hell, allegiance! Vows, to the blackest devil!
So Claudius was right—Laertes does assume Claudius is complicit in some way. Gertrude tries to assure Laertes that Claudius is guiltless, as does Claudius. The king asks Laertes to come with him—and find some of Laertes's friends—to hear corroboration.
Make choice of whom your wisest friends you will,
And they shall hear and judge ’twixt you and me.
Later in the play, Laertes reappears, apprised of the fact that Hamlet, not Claudius, killed Polonius.