According to the Catholic Church, how did Paul become a saint? In the eyes of the Catholic Church how did Saint Paul become a saint?
Was it the encounter with Jesus that made him a saint? Or was it something different?
Please answer exactly where he became one, or what the process was.
The Catholic Church honors the Apostle St Paul as a Pillar of the Church and as a martyr.

The Church celebrates two  major events in the life of the Apostle. On January 25, Catholics celebrate the Conversion of St Paul. The martyrdoms of both Saints Peter and Paul is commemorated on the Feast of Saints Peter and Paul, June 29.

The moment that changed the persecutor Saul into Paul, the follower of Jesus was when he encountered Jesus on the road to Damascus. This was the life altering moment of Saul into the person we know as St Paul!


  Paul’s entire life can be explained in terms of one experience—his meeting with Jesus on the road to Damascus. In an instant, he saw that all the zeal of his dynamic personality was being wasted, like the strength of a boxer swinging wildly. Perhaps he had never seen Jesus, who was only a few years older. But he had acquired a zealot’s hatred of all Jesus stood for, as he began to harass the Church: “...entering house after house and dragging out men and women, he handed them over for imprisonment” (Acts 8:3b). Now he himself was “entered,” possessed, all his energy harnessed to one goal—being a slave of Christ in the ministry of reconciliation, an instrument to help others experience the one Savior.
  
  One sentence determined his theology: “I am Jesus, whom you are persecuting” (Acts 9:5b). Jesus was mysteriously identified with people—the loving group of people Saul had been running down like criminals. Jesus, he saw, was the mysterious fulfillment of all he had been blindly pursuing.
  
  From then on, his only work was to “present everyone perfect in Christ. For this I labor and struggle, in accord with the exercise of his power working within me” (Colossians 1:28b-29). “For our gospel did not come to you in word alone, but also in power and in the Holy Spirit and [with] much conviction” (1 Thessalonians 1:5a). - American Catholic .Org.


As for the title of saint goes, the Early Church only recognized martyrs as saints. St Paul made the ultimate witness of his faith when he was martyred in Rome some time around 66 AD.


  The early Church understood that only the Christian who followed Christ perfectly would go immediately into the heavenly Jerusalem. Others would enter the purifying fires of purgatory "to be made perfect," from which they would not depart until they had "paid the last penny" (Mt 5:26, 1 Cor 3:13, 15). Since perfection was conformity to Christ in His death, a process begun at baptism, the martyr (literally, witness) for Christ was seen to have achieved the goal. Thus, during the age of persecution (from Pentecost to 311 AD) esteem for those Christians who had been killed in hatred of the faith (in odium fidei) lead Christians to extol their example of heroic witness to Christ, to guard and preserve their relics (the trophies of victory over death), and to celebrate the anniversary of their birthday into eternal life. The Circular Letter of the Church of Smyrna on the Martyrdom of St. Polycarp (155 AD) illustrates this esteem perfectly. - The History of Canonization.