Popes are elected by the College of Cardinals meeting in Conclave when the Apostolic See falls vacant.
Pope Paul VI significantly changed the rules for conclaves in 1975 when he promulgated the Apostolic Constitution Romano Pontifico Eligendo. He excluded all cardinals 80 years old or over from the conclave and made provision to prevent any bugging of the Sistine Chapel.
It was according to these rules that Albano Luciano, Patriarch of Venice, was elected Pope John Paul I and that a little over a month later, Karol Wojtyla, Cardinal Archbishop of Krakow, was elected Pope John Paul II.
Pope John Paul II himself promulgated a whole new set of rules in 1996 in the Apostolic Constitution Universi Dominici Gregis.
He has not departed radically from the traditional structure. But he has made some significant changes:
The maximum number of Cardinal Electors allowed at any one time is 120. The Pope cannot raise more than 120 men under 80 to the Cardinalate at any one time. (Of course, being Pope, he can also dispense himself with compliance with that rule! On the last two occasions, the Pope named new cardinals soon after the number of electors fell below 120. There were as high as 135 electors at some stages.) As at April 2005, there are 117 Cardinals eligible to vote in Conclave. (Only 115 of them entered the 2005 Conclave, as two of them were too ill to travel to Rome for the Conclave.)
The Pope dies
When the Pope dies, the Cardinal Camerlengo (currently Eduardo Cardinal Martinez Somalo) must verify the death, traditionally by calling the Pope three times by his name without response (although this is only a ritual &emdash; the death is verified by medical staff). He must then authorize a death certificate and make the event public by notifying the Cardinal Vicar for the Diocese of Rome (currently Camillo Cardinal Ruini). The Camerlengo then seals the Pope's private apartments. He would also arrange for the "ring of the fisherman" and the papal seal to be broken. He then makes preparations for the Papal funeral rites and the novemdieles, the nine days of mourning.
During the interregnum, it is the Camerlengo who is responsible for the government of the Church. He must arrange the funeral and burial of the Pope. He directs the election of a new pope, assisted by three Cardinals, elected by the College of Cardinals, with three replacement Cardinals elected every three days.
All heads of the dicasteries of the Roman Curia are suspended from exercising their authority during the interregnum (and are expected to resign their posts immediately on the election of the new Pope). The only exceptions to this are the Cardinal Camerlengo, the Cardinal Vicar of Rome, the Major Penitentiary (James Cardinal Stafford), the Cardinal Archpriest of St Peter's Basilica and the Vicar-General for Vatican City (both offices are held by Francesco Cardinal Marchisano). These continue in their posts during the interregnum.
After 15-20 days of "General Congregations", sermons at their Titular Churches on what kind of Pope the Church needs, and mourning for the Pope after his funeral, the Cardinal Electors enter the Conclave to choose which of them will emerge as Holy Roman Pontiff.
The Cardinals must take an oath when they first enter the Conclave that they will follow the rules set down by the Pope and that they will maintain absolute secrecy about the voting and deliberations. The penalty for disclosing anything about the conclave that must be kept secret is automatic excommunication.
The Cardinals all take seats around the wall of the Sistine Chapel and take a ballot paper on which is written "Eligo in summum pontificem" -- "I elect as supreme Pontiff...". They then write a name on it, fold it, and then proceed one by one to approach the altar, where a chalice stands with a paten on it. They hold up their ballot high to show that they have voted, then place it on the paten, and then slide it into the chalice. The votes are then counted by the Cardinal Camerlengo and his three assistants. Each assistant reads the name, reads the name aloud, writes it down on a tally sheet and then passes it to the next assistant. The third assistant runs a needle and thread through the centre of each ballot to join them all together. The ballots are then burned, as well as all notes made. If a new Pope has been elected, the papers are burned with chemicals (it used to be wet straw) to give white smoke. Otherwise, they give off black smoke, so that the waiting crowds, and the world, know whether their new Holy Father will soon emerge from the Sistine Chapel. On 6 April 2005, it was announced that, in addition to the white smoke, the bells of St Peter's Basilica will be rung to signal the election of the new Pope. This will avoid any doubt about whether the smoke is white or black.
Until the conclaves of 1978, each Cardinal was provided a throne and a table and a canopy (or baldachino) over their heads. Paul VI abolished the practice because, with the internationalization of the College of Cardinals, there was simply no room any more. Whereas there were only 80 electors before then, the number had risen to 120. The thrones used to be arranged in two rows, along the wall facing each other. The canopies and thrones symbolized that, during the sede vacante when there is no Pope, the Cardinals all share responsibility for the governance of the Church. To further this symbolism, once the new Pope was elected and announced the name he would use, the other Cardinals would pull on a cord and the canopy would collapse, leaving just the new Pope with his canopy aloft.
To be elected Pope, one Cardinal must receive at least two-thirds of the votes. Except that, under the new rules established by Pope John Paul II, if a certain number of ballots have taken place without any Cardinal being elected Pope, then the Cardinals may then elect by simple majority. This is an important change and may well be the most important change made. In the past, it has often been the case that a particular candidate has had solid majority support but cannot garner the required two-thirds majority, eg, because he is too conservative to satisfy the more moderate Cardinals. Therefore a compromise candidate is chosen, either an old Pope who will die soon and not do much until the next conclave (which is what was intended with John XXIII!) or someone not so hard-line wins support. The difference now will be that if, in the early ballots, one candidate has strong majority support, there is less incentive for that majority to compromise with the cardinals who are against their candidate and they simply need to sit out 30 ballots to elect their man. This may well see much more "hard-line" Popes being elected. There will also be far less incentive for the Cardinals to finish quickly as in the past. After such a long papacy, they may need time to arrive at a strong consensus on what type of papacy the Church now needs. They will also be staying in comfortable lodgings, rather than sleeping in foldaway cots in hallways and offices in the Sistine Chapel. On the other hand, the Cardinals will be reluctant for it to appear as if they are deeply divided, so there will still be an overriding desire to have a quick conclave. (No conclave in the last 200 years has lasted more than 5 days.)
The cardinals vote on the afternoon of the first day, then twice each morning and twice each afternoon. If they have not elected someone within the first three votes, then they may devote up to a day to prayer and discussion before resuming. They may do the same every seven unsuccessful votes after that.
The Cardinals are not permitted any contact with the outside world: no mobile phones, no newspapers or television, no messages or letters or signals to observers. There will be regular sweeps of all relevant areas for listening devices. The Cardinals will for the first time be able to move freely within Vatican City (eg, taking a walk in the Vatican Gardens, or walking from the Domus Sanctae Marthae to the Sistine Chapel). Workers in Vatican City continue to go about their business during the Conclave. If they run into a Cardinal, they are forbidden from speaking to him.
Once a Cardinal has received the required number of votes, the Dean of the College of Cardinals asks him if he accepts election and by what name he wishes to be called as Pope. On giving assent, the Cardinal immediately becomes Pontifex Maximus, the Holy Roman Pontiff. In the unlikely event that the Cardinal chosen is not yet a bishop, the most senior Cardinal present (the Dean or Sub-Dean usually) immediately performs the ceremony to consecrate the new Pope as a bishop.
The Cardinals then pledge their obedience to His Holiness in turn. The Pope vests in his Pontifical clericals (white soutane and skull cap) -- the Italian family business in Rome that makes all the Papal vestments has several different sizes prepared in readiness for His Holiness, no matter what his shape or size!
The Proto-Deacon of the College of Cardinals (currently Cardinal Medina Estevez) then steps onto the main balcony of the Vatican and declares to the World: "Habemus Papam!" "We have a Pope!" and tells the waiting world who has been chosen as the new pope and the name he has decided to take as Pope. His Holiness then appears on the Balcony and delivers his Apostolic Blessing to the city of Rome and to the World.
The Pope can ask the Cardinals to remain in Conclave one last evening. Both John Paul I and John Paul II did so, and spent their first evening as Pope with the Cardinals. A suite in the Domus Sanctae Marthae is kept free for the new Pope to stay in instead of returning to the room he occupied as a voting Cardinal during the Conclave.
Within a short time of his election, before the Cardinals return home, a formal ceremony of inauguration takes place at which the woollen pallium is bestowed upon him. The choir chants "Tu es Petrus" (Thou art Peter), the words Christ spoke to Peter when He told him he was the Rock on which Jesus would build His Church and asked him to feed His sheep.
One of the few things Pope John Paul I managed to do in his short papacy was to abolish the traditional Papal Coronation, which Pope John Paul II did not resurrect. Traditionally, the Pope would be carried around St Peter's Square on the Sedia Gestatoria (the Papal Throne) and have the Papal Tiara placed on his head. These last two popes have done away with the monarchic symbolism of the papacy (including the use of the Royal "we") in favour of a heightened concentration of their role as "Servus Servorum Dei" -- Servant of the servants of God. It remains to be seen whether a future Pope restores some form of papal coronation ceremony, even if it does not involve a full return to some of the earlier monarchic rituals.
More information on what happens when the Pope dies
What's in a name? - Information on papal names
The Pope & Papacy
Universi Dominici Gregis - full text of the rules govening the processes involved in the Pope's death and funeral, the interregnum and the conclave to elect the new Pope
Catholic Pages Directory: Pope & Papacy
Catholic Pages Directory: Papal Elections
St Malachy's Prophecy of the Popes