About how long has Hamlet's father been dead?

Once Hamlet had received word that the King had died, he began his journey home. By the time he arrives in Elsinore, over a month has passed and his mother and uncle are married. By the time the events of the play occur, it has been two months since the King's death.

HAMLET
Within a month, 
Ere yet the salt of most unrighteous tears 
Had left the flushing in her galled eyes, 
She married. O, most wicked speed, to post
With such dexterity to incestuous sheets!
(Act I, Scene 2)

HAMLET
O heavens! die two months ago, and not forgotten
yet? Then there's hope a great man's memory may
outlive his life half a year.
(Act III, Scene 2)