He tells him that he knew him, and that he was a fellow of most infinite jest, of most excellent fancy. In other words, he was a funny guy. He also used to carry Hamlet piggyback when Hamlet was a child.
Hamlet asks Horatio to, "tell my story"
Hamlet prevents Horatio from drinking what's left of the wine that Claudius poisoned, because Hamlet wants Horatio to tell people his side of the story.
Horatio.
Hamlet asks Horatio to recount his tale.
He asks Horatio to tell his story.
Horatio lives to tell his friend's story.
Hamlet asks Horatio to minutely observe the reactions of Claudius while watching the play. Hamlet considers that his own opinion may be prejudiced, thus he appoints Horatio as a neutral or third party observer to ensure an objective view.
Horatio - Hamlet - was created in 1600.
Horatio tell HAmlet that after midnight his father ghost shows up
He tells Horatio to "draw his breath in pain," to tell Hamlet's story.
Horatio plans to go meet Hamlet at Elsinore, which he does in Act 1 Scene 2. Horatio plans to meet Hamlet on the battlements, which he does in Act I Scene 4. Horatio plans to meet Hamlet at the play, and does in Act 3 Scene 2. Horatio has no plans to meet Hamlet in England.
Hamlet: My father! Methinks I see my father! Horatio: Where, my lord? Hamlet: In my mind's eye, Horatio.