How does Horatio die in hamlet?

Answer 1

Horatio didn't die in Hamlet.

The following is from Wikipedia (search was for Hamlet with Horatio):

Horatio is present through most of the major scenes of the play, but Hamlet is usually the only person to acknowledge that he is present; when other characters address him, they are almost always telling him to leave. He is often in scenes that are usually remembered as soliloquies, such as Hamlet's famous scene with the skull of Yorick. Horatio is also present during the mousetrap play, the discovery of Ophelia's madness (though the role of an anonymous gentleman-courtier has been substituted in this scene), Hamlet's display at Ophelia's grave, and the all-important final scene. He is the only major main character to survive all the way to the end of the play.

In performance, the part of Horatio is the only major part that can't be doubled, i.e. that can't be played by an actor who also plays another character, since he is present in scenes involving nearly every character.

Answer 2

He doesn't usually. In most productions he is alive at the end. In one extremely dark production, Fortinbras's last line, "Go, bid the soldiers shoot." was interpreted as an order to a firing squad who then execute Horatio.