How does grace dawn in the helpless soul?
God's preventing (or prevenient) grace lightens the effects of original sin even before we are aware of our need for God.
Catechism for the Global Methodist Church, question 50
37And because he loved your fathers, he chose his seed after him and brought you out before him with his great strength from Egypt.
6For you are a people holy to the LORD your God; the LORD your God has chosen you to be a people for his own possession out of all the peoples that are upon the face of the ground. 7It was not because you were more numerous than all the peoples that the LORD set his affection on you and chose you, for you were the fewest of all the peoples. 8But it was because the LORD loved you and kept the oath he swore to your fathers that he brought you out with a mighty hand and redeemed you from the house of slavery, from the power of Pharaoh king of Egypt.
2For you are a people holy to the LORD your God. The LORD has chosen you to be a people for a possession to him out of all the peoples that are upon the face of the earth.
45That you may become sons of your Father who is in the heavens, for he causes his sun to rise upon evil ones and upon good ones, and he causes rain to fall upon just ones and upon unjust ones.
20And he arose and came to his father. But while he was still far off, his father saw him and was moved with compassion, and he ran and fell upon his neck and kissed him.
44No one is able to come to me unless the Father who sent me draws him, and I will raise him up on the last day.
5I am the vine; you are the branches. The one who abides in me and I in him bears much fruit, for apart from me you can do nothing.
9The Lord does not delay the promise, as some count slowness, but has patience toward you, not planning that any should perish but that all should come to repentance.
11For the grace of God has appeared, saving for all people. 12It trains us to renounce ungodliness and worldly desires and to live self-controlled, upright, and godly lives in the present age.

Question 50 begins the catechism's walk through the stages of grace named in question 49, and it starts where ¶102 of the Book of Doctrines and Discipline starts. ¶102.3 defines God's "prevenient or preventing grace" as "the first dawning of grace in the soul," a phrase borrowed from Wesley, "mitigating the effects of original sin, even before we are aware of our need for God." The catechism's answer is a close paraphrase of that sentence. The older word "preventing" keeps its Latin sense of going before: this is the grace that arrives before any human response is possible.
The question calls the soul "helpless" because it cannot move toward God on its own. Jesus says, "No one is able to come to me unless the Father who sent me draws him" (John 6:44), and "apart from me you can do nothing" (John 15:5). The references answer that the Father does draw, and draws without waiting for merit. Moses tells Israel, (Deuteronomy 7:7); they were chosen "because the LORD loved you and kept the oath he swore to your fathers" (Deuteronomy 7:8). The parable of the prodigal shows the same order: "while he was still far off, his father saw him and was moved with compassion, and he ran and fell upon his neck" (Luke 15:20).
The catechism also insists that this first grace is universal. Jesus says the Father "causes his sun to rise upon evil ones and upon good ones" (Matthew 5:45). Paul writes that "the grace of God has appeared, saving for all people" (Titus 2:11). Peter says the Lord is "not planning that any should perish but that all should come to repentance" (2 Peter 3:9). ¶102.1 puts it as a celebration of "the universal love of God in affirming that Christ died for all people."
This teaching gives a Methodist a way of understanding his own story before conversion and a way of regarding his neighbor. The restlessness, the sense of being sought, the conscience that would not quite go quiet: the church names those as God already at work. And the neighbor who shows no interest in God is someone on whom the sun is still rising and toward whom the Father is still patient (2 Peter 3:9).