Matthew 28:19 is a biblical passage sometimes misunderstood with regard to the Trinity doctrine. Jesus is quoted as telling His disciples, "Go therefore and make disciples of all the nations, baptizing them in ['into,' Greek eis] the name of the Father and of the Son and of the Holy Spirit."
Remember the important principle that the Bible interprets the Bible. What this particular passage shows us is that the process of baptism and entering God's family involves the Father, the Son and the Holy Spirit. It is not a description of the nature of God.
Notice Acts 2:38: "Then Peter said to them, 'Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit." After real repentance and being baptized, the example from Scripture is that a minister lays his hands on the repentant person and he or she receives the Holy Spirit directly from God (Acts 8:14-17).
Important as it is, baptism alone is not sufficient. It must be followed by the biblically mandated laying on of hands for the receiving of the Holy Spirit—the seed of eternal life (Acts 19:1-6). We cannot partake of God's nature (2 Peter 1:4) without first being begotten of the Father by the Holy Spirit, which imparts that divine nature.
Christ's instruction in Matthew 28:19 presumes that, before being baptized, believers will learn of God the Father, His Son and the Holy Spirit. At baptism, they enter into a personal family relationship with God the Father and the Son through the Holy Spirit, thereby receiving the name of God (compare Ephesians 3:14-15).
Note again that all three—Father, Son and Holy Spirit—are acknowledged as being involved in this process. But that does not mean all three are divine persons in a Trinity. To claim that Matthew 28:19 establishes one God in three persons goes far beyond the actual words of the verse. And other verses show such a notion to be utterly false.