What is the mystery of the Trinity?
God is Father, Son, and Holy Spirit, distinct but inseparable, eternally one in essence and power.
Catechism for the Global Methodist Church, question 3
21It came to pass then, while all the people were being baptized and Jesus had been baptized and was praying, that the heaven was opened. 22And the holy Spirit descended in bodily form like a dove upon him, and a voice came from heaven: "You are my beloved son; I am well pleased in you."
26When the counsellor comes, whom I will send to you from the father, the spirit of truth who proceeds from the father, he will testify about me.
33Being therefore exalted at the right hand of God, and having received from the Father the promise of the Holy Spirit, he poured out this that you yourselves see and hear.
9You, however, are not in the flesh but in the Spirit, provided that the Spirit of God dwells in you. Anyone who does not have the Spirit of Christ does not belong to him. 10If Christ is in you, the body is dead because of sin, yet the Spirit is life because of righteousness. 11If the Spirit of the one who raised Jesus from the dead dwells in you, then the one who raised Christ Jesus from the dead will also give life to your mortal bodies through his Spirit dwelling in you.
13All the holy ones greet you. 14The grace of the Lord Jesus Christ and the love of God and the fellowship of the holy Spirit be with you all.
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!'
18that through him we both have access in one Spirit to the Father.
4But when the kindness and the benevolence of God our Savior appeared, 5not by works that we did in righteousness, but according to his own mercy he saved us, through the washing of regeneration and renewal of the Holy Spirit, 6whom he poured out on us richly through Jesus Christ our Savior,
14how much more will the blood of Christ, who through the eternal Spirit offered himself without blemish to God, cleanse our conscience from dead works so that we may serve the living God.
2according to the foreknowledge of God the Father, in the holiness of the Spirit, toward obedience and sprinkling of the blood of Jesus Christ. May grace and peace be multiplied to you.
Question 2 named God as the Holy Trinity. This question asks what that name means, and the catechism answers with the closing sentence of Article I of the Confession of Faith: "We believe the one God reveals himself as the Trinity: Father, Son and Holy Spirit, distinct but inseparable, eternally one in essence and power." Article I of the Articles of Religion says the same in older language: in the unity of the Godhead there are three persons, of one substance, power, and eternity.
The scriptures the catechism cites show the three persons acting together. At the Jordan, Jesus is baptized, "the holy Spirit descended in bodily form like a dove upon him, and a voice came from heaven: 'You are my beloved son'" (Luke 3:21-22). Jesus later promises the Spirit: (John 15:26). At Pentecost the risen Son, "having received from the Father the promise of the Holy Spirit," pours out that Spirit on the church (Acts 2:33).
Inseparable and one in essence and power mean that these three are never three gods and never work apart from one another. Paul calls the same indwelling presence "the Spirit of God," "the Spirit of Christ," and "the Spirit of the one who raised Jesus from the dead" (Romans 8:9-11). The Father "sent forth his Son," and then "sent the Spirit of his Son into our hearts, crying, 'Abba! Father!'" (Galatians 4:4-6). Peter greets believers chosen "according to the foreknowledge of God the Father, in the holiness of the Spirit, toward obedience and sprinkling of the blood of Jesus Christ" (1 Peter 1:2), and Hebrews sets all three in the one sacrifice: (Hebrews 9:14).
This doctrine shapes how a Methodist prays. Ephesians 2:18 gives the pattern: "through him we both have access in one Spirit to the Father." Prayer goes to the Father, through the Son, by the Spirit. The blessing Paul closes his letter with names all three: (2 Corinthians 13:14). Titus describes the same movement in baptism: (Titus 3:5-6).