Courage comes through conviction, and conviction comes through study.
When we gain understanding of Bible doctrines, beginning with God's plan of salvation, the Holy Spirit uses that knowledge to produce conviction. Those people who are unsaved are headed for Hell, and we know the answer to their dilemma. This knowledge should produce a love in our hearts for all, the saved as well as the unsaved. It is God's will that we devote our lives to acquainting ourselves with the person and work of Jesus Christ. Also, Paul requested the prayer of other believers and no doubt prayed for himself for courage and strength when proclaiming the gospel of grace.