How does the Spirit work in the Church?
He comforts, sustains and empowers the faithful and guides us into all truth.
Catechism for the Global Methodist Church, question 24
25I have spoken these things to you while I remain with you. 26The counsellor, the holy spirit whom the father will send in my name, that one will teach you all things and will remind you of all that I said to you.
12I still have many things to say to you, but you cannot bear them now. 13When that one comes, the spirit of truth will guide you in all truth. For he will not speak from himself, but whatever he hears he will speak, and he will report to you the coming things. 14That one will glorify me, because he will take from what is mine and will report to you. 15All that the father has is mine. For this reason I said that he takes from what is mine and will report to you.
2For the law of the Spirit of life in Christ Jesus has set you free from the law of sin and death. 3For what was impossible for the law, in which it was weak through the flesh, God did by sending his own Son in the likeness of sinful flesh and concerning sin; he condemned sin in the flesh. 4In order that the righteous act of the law might be fulfilled in us who walk not according to the flesh but according to the Spirit. 5For those who are according to the flesh set their minds on the things of the flesh, but those who are according to the Spirit set their minds on the things of the Spirit. 6For the purpose of the flesh is death, but the purpose of the Spirit is life and peace. 12So then, brothers, we are debtors, not to the flesh, to live according to the flesh. 13For if you live according to the flesh you are about to die, but if by the Spirit you put to death the actions of the body you will live. 14For all who are led by the Spirit of God, these are sons of God. 15For you did not receive a spirit of slavery again toward fear, but you received a spirit of adoption as son, in which we cry, "Abba, Father." 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. 26Likewise the Spirit also helps our weakness. For what we should pray as we ought we do not know, but the Spirit itself intercedes with groanings too deep for words. 27And the one who searches the hearts knows what is the mind of the Spirit, that according to God he intercedes for the saints.
4Now there are varieties of gifts, but the same Spirit. 5And there are varieties of services, but the same Lord. 6And there are varieties of workings, but the same God who activates all things in all. 7To each is given the manifestation of the Spirit for what is profitable. 8For to one through the Spirit is given the word of wisdom, and to another the word of knowledge according to the same Spirit. 9To another faith by the same Spirit, to another gifts of healings by the one Spirit. 10To another workings of powers, to another prophecy, to another discernments of spirits, to another various kinds of tongues, to another the interpretation of tongues. 11All these the one and the same Spirit activates, distributing to each one individually just as he wills.
16I say then: walk by the Spirit, and you will not gratify the desire of the flesh. 17For the flesh desires against the Spirit, and the Spirit against the flesh; for these are opposed to each other, so that you may not do whatever you want. 18But if you are led by the Spirit, you are not under the law. 19The works of the flesh are evident: sexual immorality, impurity, sensuality. 20Idolatry, sorcery, enmities, strife, jealousy, fits of anger, rivalries, dissensions, factions. 21Envyings, drunkenness, carousing, and things like these, of which I forewarn you, just as I forewarned you, that those who practice such things will not inherit the kingdom of God. 22The fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness. 23Gentleness, self-control; against such things there is no law. 24Those who belong to Christ Jesus have crucified the flesh with its passions and desires. 25If we live by the Spirit, let us also keep in step with the Spirit.

The final sentence of Article III of the Confession of Faith supplies this answer nearly verbatim: "He comforts, sustains and empowers the faithful and guides them into all truth." This question describes what he does among those who now belong to Christ.
The word comforts comes from the upper room. Jesus promised "the counsellor, the holy spirit whom the father will send in my name," who "will teach you all things and will remind you of all that I said to you" (John 14:26). He also promised guidance: (John 16:13), and "he will take from what is mine and will report to you" (John 16:14). The Spirit's teaching always points back to Christ. Sustains is the Spirit's help in weakness. (Romans 8:26), and "the Spirit himself testifies together with our spirit that we are children of God" (Romans 8:16).
Empowers covers two things Paul describes at length. First, holiness: "if by the Spirit you put to death the actions of the body you will live" (Romans 8:13), and (Galatians 5:16). The result is "the fruit of the Spirit," which is "love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control" (Galatians 5:22-23). Second, gifts for service: "there are varieties of gifts, but the same Spirit" (1 Corinthians 12:4), and "to each is given the manifestation of the Spirit for what is profitable" (1 Corinthians 12:7), distributed "to each one individually just as he wills" (1 Corinthians 12:11).
This is where the Wesleyan doctrine of sanctification lives. ΒΆ102 of the Book of Doctrines and Discipline describes sanctification as "the process by which the Holy Spirit increasingly cleanses the heart in Christlikeness to put to death the carnal nature in an ever-increasing abundance of the fruit of the Spirit." A Methodist should therefore expect the Spirit to be active in the ordinary means of grace: the preached word, the Lord's Supper, prayer, fasting, scripture, and Christian conference. In each of these he comforts the grieving, sustains the weary, equips the willing, and keeps the church tethered to the truth of Christ.