Vatican City (or Città del Vaticano as the locals call it!) is one of the smallest States in the world. Here are some geographical and political facts about Vatican City State.
The Roman Curia by Paul McLachlan
The Pope's "Government" of Vatican City State (as Head of State) and of the Catholic Church (as Pontiff) is assisted by the Roman Curia -- the Congregations and Dicasteries set up as his "Ministries". This article explains what each of the Disasteries is and what its role is in the governance of the Church or Vatican City State.
The Vatican Diplomatic Corps by Paul McLachlan
As a sovereign State, the Holy See sends diplomatic representatives to other nations (called Nuncios) and receives Ambassadors from other countries. This article from the Vatican Information Service provides some background on the Vatican Diplomatic Corps.