
The above article is a good short summary of traditional Christian
teaching concerning the death of Mary.  
Also very good is "Re: Question about the Virgin Mary" by Micheal D.
Walker.  He tells the story very well.
I would like to add that in the Eastern Orthodox Church we celebrate "The
Dormition (or falling asleep) of the Theotokos (the mother of God)".  The
Icon for this day shows Mary lying on a bed surrounded by the Apostles
who are weeping.  Christ, in his resurrected glory, is there holding what
seems to be a small child.  This is, in fact, Mary's soul already with
Christ in Heaven.  The Assumption of Mary is one more confirmation for us
as Christians that Christ did indeed conquer death.  It forshadows the
general resurrection on the last day.  The disciples were not surprised
to find Mary's body missing from the grave.  She was the Mother of the
Savior.  She was the first of all Christians.  She gave birth to the Word
of God.  If it were not for her we would not be saved.  This is why we
pray in the Orthodox Church, "Through the prayers of the Theotokos,
Savior save us."