Paul was personally converted to Christianity by Jesus himself after his resurrection. Paul was not taught by the other apostles but was educated by the same Master who educated them.
His approach to prayer would have been the same as the other apostles.
At Phillipians 4:6-7...Paul wrote....
"Do not be anxious over anything, but in everything by prayer and supplication along with thanksgiving, let your petitions be made known to God; 7 and the peace of God that surpasses all understanding will guard your hearts and your mental powers by means of Christ Jesus."
This is what Paul said we need to do....to supplicate God.....to give him our petitions.....but never to forget to think him for the many blessing we enjoy, in spite of our troubles.