On the morning of February 11, 2013, the Vatican announced the pending resignationof Pope Benedict XVI. Benedict will be the first Pope to relinquish the office since Gregory XII did so in 1415 to end the Western Schism and the first do so on his own initiative since Pope Celestine V in 1294.
This is a short introduction to Papal Conclaves and how they work.
The Pope, the Bishop of Rome, is chosen by the College of Cardinals, convened and sequestered in St. Peter’s for the election. Since 1846 the voting itself occurs in the Sistine Chapel. According to current Canon Law, cardinal electors are those cardinals under the age of 80.
Conclave comes from two Latin words: cum and clavis, best translated as locked with a key. It refers to both the locked place where the election takes place (the Sistine Chapel) and the gathering itself.
The process dates back to 1059 C.E. and replaced the earlier system of selecting a bishop via the consensus of the clergy and laity of the diocese. Currently the rules require a two-thirds super majority of the College as well as the consent of the elected.
The Dean of the College of Cardinals (currently Cardinal Angelo Sardano) convenes the Conclave, which begins fifteen to twenty days after the death of a Pope. Since the papacy will become vacant on February 28th, most interpret Canon Law to mean the Conclave begin fifteen to twenty days later. Recent press releases suggest that indeed the Conclave may begin before March 15th. The actual date may depend on the speed which the members of the College of Cardinals arrive in Rome.
Procedures followed during the Conclave are specified in the Ordo Rituum Conclavis (Order of Rites for the Conclave). It is possible that these rites are changed by Benedict through a Moto Propio (literally “on his own impulse,” meaning a document issued by the Pope on is own initiative and personally signed by him) before February 28th.
The Conclave will begin with Mass, followed by the preliminary sessions, presided over by the Dean of Cadinals, to clarify the election procedures. Then all not belonging to the College of Cardinals are dismissed and the Cardinals are sealed in the Sistine Chapel. 
For each ballot the Cardinals receive rectangular cards with the words Eligio in summum pontificem (I elect as supreme pontiff) printed at the top. Each cardinal prints the name of his choice on the card, folds it down the middle, and then places the card in a chalice.
After each vote the ballots are burned. Chemicals are added to make the smoke black (meaning no pope is yet selected) or white (meaning there is a pope). The only requirement is that the Pope be a baptized male.
Once selected, if not already a bishop, the new Pope is immediately ordained (the last non-bishop to be selected Pope was Urban VI elected in 1378). The Cardinals present then pledge their support to the new pope. The Dean of Cardinals ask what name the new pope chooses. The oldest Cardinal present announces the choice to the City of Rome and the world with the following Latin phrase: Annuntio vobis gaudium magnum! Habemos Papam! (I announce to you a great joy! We have a pope!).