Enter Francisco at his post. Enter to him Barnardo, then Horatio and Marcellus:
The play opens in the dark and cold. Francisco is standing watch on the guard platform of the castle at Elsinore. In films, this place is usually depicted as being very high on the walls of the castle, with a view of the dark sea. Francisco isn't feeling well and it's very cold, so he's on edge.
Barnardo, who is to take Francisco's place, comes up onto the platform and looks around. He can't see anything clearly, or perhaps he's already looking for the Ghost, so he asks, Who's there?" (1.1.1). (His "Who's there?" is also thematic; throughout the play, there are questions about who is behind a curtain or who is behind a mask that is shown to the world.)
Francisco answers, "Nay, answer me" (1.1.2), meaning "I'm on guard here, and I get to ask the questions." Barnardo identifies himself, and Francisco is glad to see him, because "'Tis bitter cold, / And I am sick at heart" (1.1.8-9).
As Francisco is leaving, Horatio and Marcellus come up onto the platform. Marcellus, like Barnardo, is a common soldier who has seen a ghost. Both of them want someone else to confirm that there is indeed a ghost, as any of us might want to do if we thought we had seen an alien from outer space. Tonight Marcellus and Barnardo have brought along Horatio, who is an educated gentleman, to see the ghost, too. They don't want to think that they are merely seeing things, but that is just what Horatio thinks; Marcellus says, "Horatio says 'tis but our fantasy" (1.1.23).
The Ghost looks like the king who just died, old Hamlet, the father of Hamlet. He is in armor and a horrifying figure. Horatio, whose doubts about the reality of the Ghost are now wiped away, says "it harrows me with fear and wonder" (1.1.44). Marcellus and Barnardo want Horatio to speak to the Ghost, and Horatio tries, asking the Ghost what it is, but the Ghost disappears.
Then the men try to figure out why the Ghost has appeared. Marcellus thinks it must have something to do with the preparations for war that are going on in Denmark. Horatio is able to fill him in on that: The dead King, old Hamlet, engaged in single combat with Fortinbras, King of Norway, killed him, and won certain lands in the battle. Now Fortinbras, son of the dead king, has "shark'd up a list of lawless resolutes" (1.1.98) to form an army of irregulars, so that he can win back the lands that his father lost. (This young Fortinbras is not King of Norway. His uncle is king, as Hamlet's uncle is now King of Denmark.)
Not only that, but Horatio adds that the appearance of the Ghost reminds him of what he has read about the portents in Rome, just before the assassination of Julius Caesar, when "The graves stood tenantless and the sheeted dead / Did squeak and gibber in the Roman streets" (1.1.115-116).
After the Ghost has disappeared, Marcellus is a little ashamed of what he has done, saying "We do it wrong, being so majestical, / To offer it the show of violence" (1.1.143-144).
The scene then lightens from night to dawn. Horatio reflects that the cock-crow frightened the Ghost away because no "erring spirit" can be abroad during the day, and Marcellus says that at Christmastide the cock crows all night long, so that even "the nights are wholesome." And then, in a beautiful image, it's dawn. Horatio says, "But, look, the morn, in russet mantle clad, / Walks o'er the dew of yon high eastward hill" (1.1.166-167).
Finally, Horatio and Marcellus agree that "young Hamlet" should be told of all of this, for surely the Ghost will speak to him.