God's grace comes in countless shapes and sizes. However, we can see through scripture how he works in the life of a non-believer. He first softens the hardened heart of the non-believer to receive the glorious and grace-filled gospel. He then softens their hardened heart to acknowledge their need for salvation. He then softens their hardened heart to repent of their sins and to turn away from a self-seeking life towards a God of mercy, love, kindness and forgiveness. These are all aspects of how God's grace works in the life of the non-believer...but in each of these steps, both God and the person play a role. God provides the grace, and the person responds to that grace in such a way as to move (through the power of the Holy Spirit) in a new direction.
We add nothing to God's saving grace...but by his grace, we DO play a part.
"In His message of the kingdom, Jesus announced the overwhelming, amazing wonder of God's sovereign grace reaching down to reclaim sinful people for Himself. But no one emphasized as strongly as Jesus the need for people touched by God's grace to respond with radical, world-renouncing obedience. Both the gracious initiative of God and the grateful response of human beings are necessary aspects of the gospel"
Douglas Moo | James, Eerdmans, 2000, p. 89