The election of the new Pope follows a process laid out in the Apostolic Constitution Universi Dominici gregis. When there is no Pope (known as sede vacante), the cardinals are limited in what can be done or modified during the vacancy. Part one chapter one states "the government of the Church is entrusted to the College of Cardinals solely for the dispatch of ordinary business and of matters which cannot be postponed (No. 6 Universi Dominici gregis), and for the preparation of everything necessary for the election of the new Pope."
There are over 250 cardinals who will gather in Rome, but not all are eligible to vote. All cardinals are members of the General Congregation which will meet in the days before the election to establish funeral details, attend to administrative issues, and "set the day and hour of the beginning of the voting process" (No.13i Universi Dominici gregis). Only Cardinals under the age of 80 are eligible to vote and of these, typically only 120 are selected as electors (No.33 Universi Dominici gregis).
The electors will proceed to the Sistine Chapel where they will take an oath of secrecy and remain behind sealed doors for the election. The cardinal electors are not to communicate with anyone beyond this area until the conclusion of the election (No. 44 Universi Dominici gregis). Voting is by written, secret ballots (must be rectangular in shape). Each elector writes one name, folds the ballot twice, holds it up to be seen, and then places in in a receptacle on the altar (No.66 Universi Dominici gregis). Votes are counted and tabulated immediately afterward. The number of ballots must equal the number of electors or the ballots are burned and voting begins again. Voting may take place four times per day with a one day break every three days.
If no individual receives 2/3 of the vote, the ballots are burned producing black smoke out of the chimney (installed only for papal elections) to indicate to outside observers that no pope has been selected. If an individual receives 2/3 of the vote, the election of the Roman Pontiff has occurred and the ballots are burned with a special chemical producing white smoke from the chimney. This is verification to outside observers that we have a new Pope!