How does regeneration allow us to live as children of God?
By this new birth the believer becomes reconciled to God and is enabled to serve him with the will and the affections.
Catechism for the Global Methodist Church, question 63
6And he was faithful in the LORD, and he reckoned it to him as righteousness.
5And you shall love the LORD your God with all your heart and with all your soul and with all your strength.
12And now, Israel, what does the LORD your God ask from you except to fear the LORD your God, to walk in all his ways, and to love him, and to serve the LORD your God with all your heart and with all your soul? 13You are to keep the commandment of the LORD and his statutes that I am commanding you today, for your good.
12But to all who did receive him, to those who believe in his name, he gave the right to become children of God.
16The Spirit himself testifies together with our spirit that we are children of God. 17And if children, then also heirs, heirs of God and co-heirs of Christ, if indeed we suffer with him so that we may also be glorified with him.
18And I will be a father to you, and you shall be sons and daughters to me, says the Lord Almighty.
26For you are all sons of God through faith in Christ Jesus.
4But when the fullness of time had come, God sent forth his Son, born of a woman, born under the law. 5To redeem those who were under the law, so that we might receive adoption as sons. 6And because you are sons, God has sent the Spirit of his Son into our hearts, crying, 'Abba! Father!' 7So you are no longer a slave, but a son; and if a son, then an heir through God.
5He predestined us for adoption through Jesus Christ toward himself, according to the goodwill of his will. 6For the praise of the glory of his grace, with which he favored us in the Beloved.
13For it is God who is at work in you, both to will and to work for his good pleasure.
1See what kind of love the Father has given us, that we should be called children of God: and so we are. The world does not know us because it did not know him. 10By this the children of God and the children of the devil are revealed: anyone who does not practice righteousness is not of God, nor is the one who does not love his brother.
The catechism has said what regeneration is and how it changes a person; this question asks what the changed person is now able to do. The answer is the closing sentence of the second paragraph of Article IX of the Confession of Faith: "By this new birth the believer becomes reconciled to God and is enabled to serve him with the will and the affections." ΒΆ102.2 of the Book of Doctrines and Discipline says the same in its own words, that grace "enables us to live as children of God, freed for joyful obedience."
The first half of the answer is adoption. To those who believe in Christ's name "he gave the right to become children of God" (John 1:12), and Paul explains how that right was secured: "God sent forth his Son, born of a woman, born under the law, to redeem those who were under the law, so that we might receive adoption as sons" (Galatians 4:4-5).
The second half of the answer, service "with the will and the affections," is where the Wesleyan emphasis falls. Wesley described true religion as holiness of heart and life, and the Deuteronomy references show why the heart comes first: "you shall love the LORD your God with all your heart and with all your soul and with all your strength" (Deuteronomy 6:5). Before the new birth that command exposes a person's inability, since Article VII of the Confession of Faith says fallen man is "inclined to evil." After the new birth the same command becomes possible, because "it is God who is at work in you, both to will and to work for his good pleasure" (Philippians 2:13). The willing and the working are both God's gift, which is what the catechism means by "enabled."
For a Methodist this teaching turns obedience into family life. (1 John 3:1) John gives a plain test of who belongs to the family: "anyone who does not practice righteousness is not of God, nor is the one who does not love his brother" (1 John 3:10). A child of God serves out of affection for the Father whose Spirit "testifies together with our spirit that we are children of God" (Romans 8:16), and Article IX of the Confession of Faith says that this affectionate service is what regeneration equips a believer to give.