Other than the Pope himself, it’s an exhaustively complex process that involves the laity, local dioceses, and a whole array of top Vatican officials and departments. Here’s a quick snapshot (note—portions excerpted or adapted from the USCCB and EWTN are noted):
(Note to readers: It might be helpful to refer to my previous post on the steps involved in canonization, while reading this.)
Petitioner – Party initiating action in canon law. In the case of a sainthood cause, the petitioner is one who asks the bishop to begin the investigation which could ultimately lead to canonization. (A bishop may also begin a cause on his own initiation.) – USCCB
Congregation for the Causes of Saints – A department of the Roman Curia, established originally as the Congregation of Rites by Pope Sixtus V in 1588. Reorganized and renamed in 1969 by Pope Paul VI, and again in 1983 by Pope John Paul II. In addition to making recommendations to the pope on beatifications and canonizations, it is also responsible for the authentication and preservation of sacred relics. – USCCB
Postulator – Person appointed to guide and oversee the cause. There are two of them. One oversees the cause at the diocesan level. The second one, resident in Rome and appointed by the Congregation for the Causes of Saints, oversees all aspects of the beatification and canonization at the Vatican level. – USCCB
Relator – Person appointed by the Congregation for the Causes of Saints to assemble the historic documentation of the particular location and era of the candidate. – USCCB
Diocesan Tribunal – After someone has been declared a Servant of God, this body concludes that the person either did or did not live a life of heroic virtue. The bishop must ultimately agree and then the results are forwarded to the Congregation for the Causes of the Saints, according to EWTN.
A diocesan theological commission – While the scientific commission rules that the cure is without natural explanation, the theological commission must rule whether the cure was a miracle in the strict sense, that is, by its nature can only be attributed to God. … The theological commission must also determine whether the miracle resulted through the intercession of the Servant of God alone. If the family and friends have been praying without cease to the Servant of God exclusively, then the case is demonstrated. – EWTN
A diocesan scientific commission – Confirms that there is no explanation for alleged miracles, (according to EWTN).
A Vatican theological commission – Working with a theological commission established by the Congregation, the Relator ensures that the Positio summarizing the life and virtues of the Servant of God is properly prepared. When the Positio is finished, the theological commission votes affirmatively or negatively on the Cause. This recommendation is then passed to the cardinal, archbishop and bishop members of the Congregation who, in turn, vote. Their vote determines whether the Cause lives or dies. If the vote is affirmative, the recommendation of a Decree of Heroic Virtues is sent to the Holy Father, whose judgment is final. As at the diocesan level, the commission must also evaluate claims to miracles. (Adapted from EWTN.)
A Vatican scientific commission – As at the diocesan level, this commission is charged with confirming that science cannot explain the apparently miraculous occurrence, according to EWTN.
Congregation for the Doctrine of Faith – In addition to the Congregation for the Causes of the Saints, this Vatican department apparently plays a key role in vetting the theology of a candidate for sainthood. In fact, this is a role it exercises with any other Vatican department. Any document emerging out the Roman Curia that involves doctrine of faith or morals must be “subjected to its prior judgment.”
Congregation for Divine Worship and the Discipline of Sacraments – This Vatican department is also involved in the canonization process. Its chief areas of concern are the cult of sacred relics and “the confirmation of heavenly patrons.” The Congregation also recently issued a decree clarifying the difference between beatification and canonization, according to the Catholic News Service.
The Role of the Pope – The pope is involved throughout the process of canonization. Indeed, he has the final word at each stage of the process. But recently efforts have been made to limit his public role to the last stage: the declaration of sainthood. According to this Catholic News Service report, this was the practice for hundreds of years, but it got muddled a bit during the end of the twentieth century. Having a Pope preside over a canonization Mass helps to emphasize the difference between a canonization and a beautification, according to the article. It’s also appropriate to have the Pope play the most prominent role at this stage, given that the declaration of sainthood is, as EWTN puts it, “an act which is protected from error by the Holy Spirit.”
The Role of the Laity – As several Harvard scholars recently noted, “[t]he process of a candidate has always been initiated from below through popular veneration in communities.” This is more carefully regulated today than it might have been hundreds of years ago, but the process generally does seem to start with the laity asking the bishop to begin the investigation.