How does God lead us to repentance?
God's convincing grace awakens in us a desire to flee the wrath to come and enables us to begin to fear God and work righteousness.
Catechism for the Global Methodist Church, question 55
1Come, and let us return to the LORD, for he has torn and he will heal us; he has struck and he will bind us up.
1And it shall be in the latter part of the days that the mountain of the house of the LORD shall be established at the head of the mountains, and it shall be lifted up above the hills, and peoples shall flow to it. 2And many nations shall go and say, "Come, let us go up to the mountain of the LORD and to the house of the God of Jacob, that he may teach us from his ways and that we may walk in his paths; for from Zion shall go forth instruction, and the word of the LORD from Jerusalem."
4Behold, his soul is swollen within him and is not upright, but the righteous one will live by his faithfulness.
20Thus says the LORD of Hosts: Peoples will still come, and the inhabitants of many cities, 21and the inhabitants of one city will go to another, saying, "Let us go at once to entreat the favor of the LORD and to seek the LORD of Hosts; I myself will go also." 22Many peoples and mighty nations will come to seek the LORD of Hosts in Jerusalem and to entreat the favor of the LORD. 23Thus says the LORD of Hosts: In those days ten men from all the languages of the nations will take hold and will grasp the wing of a Jew, saying, "Let us go with you, for we have heard that God is with you."
8And when he comes, he will convict the world concerning sin and concerning righteousness and concerning judgment.
4But God, who is rich in mercy, because of the great love with which he loved us, 5and when we were dead in the trespasses, made us alive together with Christ, by grace you are saved
9Now I rejoice, not because you were grieved, but because you were grieved into repentance; for you were grieved according to God, so that you might suffer loss in nothing from us. 10For grief according to God produces repentance that leads to salvation without regret, but the grief of the world produces death.
18Pray for us, for we are sure that we have a clear conscience, desiring to act honorably in all things.

Question 55 moves to the second of the five graces named in question 49. The answer is drawn from ¶102.4 of the Book of Doctrines and Discipline, which says that "God's convincing grace leads us to what the Bible terms 'repentance,' awakening in us a desire to 'flee from the wrath to come' (Matt. 3:7) and enabling us to begin to 'fear God and work righteousness' (see Acts 10:35)." The same paragraph records that Wesley called repentance "the porch of religion."
The word "convincing" is the older form of "convicting," and the agent is the Holy Spirit. Jesus promises that when the Spirit comes "he will convict the world concerning sin and concerning righteousness and concerning judgment" (John 16:8). The conviction produces a particular kind of sorrow. Paul told the Corinthians, (2 Corinthians 7:9), and then distinguished that grief from ordinary regret: "grief according to God produces repentance that leads to salvation without regret, but the grief of the world produces death" (2 Corinthians 7:10). Hosea gives it a voice: "Come, and let us return to the LORD, for he has torn and he will heal us; he has struck and he will bind us up" (Hosea 6:1).
The answer's second clause, "to begin to fear God and work righteousness," describes the first fruits of this turning. The prophets picture nations saying, "Come, let us go up to the mountain of the LORD" (Micah 4:2), and city calling to city, "Let us go at once to entreat the favor of the LORD" (Zechariah 8:21). Habakkuk states the governing principle: "the righteous one will live by his faithfulness" (Habakkuk 2:4). Even at this early stage, the work is God's. Paul says that God, "rich in mercy," made us alive "when we were dead in the trespasses" (Ephesians 2:4-5). The desire to flee wrath is itself a gift.
For a Methodist this teaching removes the fear that conviction of sin is a sign of God's absence. The uneasy conscience, the sorrow that will not let a wrong sit quietly, and the urge to return are the Spirit at work, drawing a person onto the porch. The proper response is the one the writer to the Hebrews models: to desire "to act honorably in all things" with "a clear conscience" (Hebrews 13:18).