From Fox News:
Following the pope’s death there is a period of mourning that lasts nine days, known as the “novendiale,” which is kicked off by the pope’s funeral. After this, roughly two to three weeks following the pope’s funeral, a “conclave” is commenced inside the Sistine Chapel by the College of Cardinals to elect his successor.
During the conclave, Cardinals eligible to vote are locked inside the famous chapel where they will take secret votes to determine who is next in line for the papacy. Up to four votes per day can take place, and the voting does not stop until a majority of Cardinals select who is next up. The conclave that elected Pope Francis in 2013 took roughly 24-hours and five ballots to come to a decision. His predecessor, Pope Benedict XVI, was elected after just four ballots. However, while the process recently has been quite rapid, it can run much longer.