The Sistine Chapel is not just a beautiful place which attracts art lovers from around the world. Historically, it was the Pope's chapel and, when a current pope dies, the Sistine is the setting for the Papal Conclave. Cardinals, from around the world, get together to select one of their number to be the next pope.
Historical ballot, used in a Papal Conclave, by Cardinals of the Catholic Church who are electing a new Pope. From London Magazine, June of 1903.
Before that happens, though, a series of rituals take place inside the Vatican. After a pope dies, and is officially declared "dead" by a doctor, the Cardinal Camerlengo (that is, the chamberlain) becomes Church administrator until a new pope is selected. The Camerlengo resides in the Vatican palace while performing all of his duties. One of his duties is to personally confirm that the pope has, indeed, passed away.
Standing over the pope’s body, the Camerlengo (in Angels & Demons, the film, his name is Patrick McKenna) calls the pope three times by his personal (baptismal) name, not his papal (official) name. He may also gently tap the pope’s head with a silver hammer.
When there is no response, a veil is placed over the pope's face and the Cardinal Camerlengo declares: "The pope is dead." All of the pope’s personal belongings are removed from his apartment and the place is taped and sealed with wax.
Thereafter, the pope’s ring (called the Fisherman's Ring) is destroyed. That ring, identical in design but different for each pope, includes the pontiff’s name engraved around an image of Peter (the first pope) casting a net from a boat. After the Papal Conclave picks the next pope, he (it's always a he) will get a new ring. The destroyed ring will be buried with the pope, in his coffin.
The pope’s body is then placed inside the Sistine Chapel, for a private time with the Vatican community. Public viewing takes place inside St. Peter’s Basilica, while the formal funeral is held in St. Peter’s Square.
When the Papal Conclave convenes, the Cardinals vote for the next pope in the Sistine Chapel. Ballots are burned after each voting round.
If a new pope has not been selected, the burning smoke is black. If a new pope has been chosen, the smoke is white. Since the Cardinals are allowed no contact with the outside world, during a Papal Conclave, the color of smoke is their only way to communicate decisions.
After a new pontiff is elected, he walks to the Room of Tears, near the Sistine’s altar. There, his new white robes are waiting for him.
Usually, going into a Papal Conclave, members have an idea about the top Cardinals in the running. In Angels & Demons, those men are called Preferati. There are four, in the story, and each one is in serious trouble.