This is a good question, friend. The doctrine of Trinity means there is one, true and living God that exists eternally in three persons: God the Father, God the Son and God the Holy Spirit. These three persons share the same divine nature yet are different in role and relationship (see figure above).
Pastor Mark Driscoll of Seattle writes the following concerning the persons of the Trinity:
“Person” does not mean that God the Father or God the Spirit became human beings. Rather, it means that each memberof the Trinity thinks, acts, feels, speaks, and relates because they are persons and not impersonal forces. Further, each member of the Trinity is equally God, which means that they share the divine attributes, such as eternality, omniscience, omnipotence, and omnipresence.
[HERE is the rest of the article]
Though this definition of the Trinity appears simplistic, it is not and therefore, it is a highly confusing topic for many people. While many Christians have heard that God exists in three persons, many seem to think that God merely manifests himself as either Father, Son or Holy Spirit on different occasions. This is the theological error known as modalism. Another theological error often made is that of tritheism, which overemphasizes the distinction between the three persons of the Trinity.
In terms of prayer, I would say, feel free to pray to any persons of the Trinity, because you are praying to GOD, who exists in three persons. Here is an article (entitled "Who can we pray to?") which addresses this issue specifically.
[Answered by Pastor HM]
