In Act I, scene 1, of Hamlet, what exposition is provided in the scene? Include an explanation of the quarrel with Norway.

Act 1.1 of Shakespeare's Hamlet, is packed with information and exposition.

We learn guards are on duty, we learn their names as well as the name of Horatio, who is trusted enough to be brought along for verification purposes.  We learn that he is a "scholar."  We learn that it is midnight and very cold. 

We learn that they are in Denmark, and we learn that these same guards have seen a ghost two nights in a row, but that Horatio doesn't believe their ghost story--until he sees the Ghost himself.

When the Ghost appears, we learn that he seems to look like the dead King Hamlet. 

Concerning the Fortinbras situation, we learn that the guards are on duty primarily because of the threat of Fortinbras.  Fortinbras' father, then the king of Norway, lost lands to King Hamlet when he was killed during a battle with Denmark.  Fortinbras is now threatening to take these lands back. 

Horatio and the guards suspect that the appearance of the Ghost suggests that trouble with Fortinbras is coming.