How does preventing grace re-establish the freedom of the will?
While in our bound and helpless state, preventing grace breaks through and enables genuine response to God's further grace.
Catechism for the Global Methodist Church, question 52
17Then Elisha prayed, "O the LORD, open his eyes so that he may see." The LORD opened the young man's eyes, and he looked and saw the hills full of horses and chariots of fire all around Elisha. 20When they entered Samaria, Elisha said, "LORD, open the eyes of these men so they can see." The LORD opened their eyes, and they saw that they were inside Samaria.
8And when he comes, he will convict the world concerning sin and concerning righteousness and concerning judgment. 9Concerning sin, because they do not believe in me. 10Concerning righteousness, then, because I am going to the Father and you will see me no longer. 11Concerning judgment, then, because the ruler of this world has been judged.
37Now when they heard, they were pierced in the heart, and said to Peter and the remaining apostles, "What shall we do, men, brothers?"
31He said, "How can I, unless someone guides me?" And he invited Philip to come up and sit with him.
8And God, who knows the heart, bore witness to them by giving them the Holy Spirit just as he did to us.
30Then he brought them out and said, "Sirs, what must I do to be saved?"
Preventing grace also restores the will. ¶102.3 of the Book of Doctrines and Discipline says: "Received prior to our ability to respond, preventing grace enables genuine response to the continuing work of God's grace." Article VIII of the Articles of Religion teaches the same in Wesley's inherited language: fallen humanity "cannot turn and prepare himself, by his own natural strength and works, to faith," and therefore has "no power to do good works" without "the grace of God by Christ preventing us, that we may have a good will."
A fallen person is in a "bound and helpless state," and God breaks in on it. Elisha prayed, "O the LORD, open his eyes so that he may see," and "the LORD opened the young man's eyes, and he looked and saw" (2 Kings 6:17). At Pentecost the crowd "were pierced in the heart" and asked, "What shall we do, men, brothers?" (Acts 2:37). At Philippi the jailer asked, "Sirs, what must I do to be saved?" (Acts 16:30). In each case God's grace produced a question a bound will could never have asked, and the question was a genuine one that the asker then had to answer.
The Holy Spirit does this work. Jesus promised that the Spirit, when he comes, "will convict the world concerning sin and concerning righteousness and concerning judgment" (John 16:8). The restored freedom is a readiness to be taught; the Ethiopian official asked Philip, "How can I, unless someone guides me?" (Acts 8:31). At the Jerusalem council Peter argued from the same fact: "God, who knows the heart, bore witness to them by giving them the Holy Spirit" (Acts 15:8). God had reached the Gentiles before anyone else did.
So a Methodist can take his own responses to God seriously without taking credit for them. The desire to pray, the decision to come forward, the choice to keep a promise made at the font: each is a genuine act of a real will, and each is possible because grace went before it. God gives the freedom, and the person uses it.