How does one become a priest? First there needs to be a desire and ability to serve others. Then there's the sense that God is calling that man to serve as a priest. There also has to be discernment and evaluation by those who are responsible for the training and education of the candidate. Finally the bishop, with help from the Vocations Director and the seminary rector, decides to accept and ordain the person to serve as a priest or to recommend a different path of service. No man has a right to become a priest.
What about St. John Vianney? Well, he had the desire and ability to serve and a strong sense of vocation, but he was not able to do well in his studies for the priesthood. He had great difficulty listening to lectures in Latin. But he persevered and was eventually ordained. His zeal for the Lord also led him to become a great confessor, sitting in the confessional 11-16 hours a day reconciling God's people. Thus, he was named patron saint of priests.
What does it mean to be a priest? It means responding to God's call to serve in a special way; through ministering the sacraments, through preaching the Good News, and through leading God's people by a life of service. We are called to love and serve the world in our daily lives, but priests are called to love and serve the People of God. God has not stopped calling men to be priests; we just need to listen more carefully. All of us are responsible for fostering priestly vocations through our prayers and our encouragement.