The first thing we learned in our church’s study of the Holy Spirit is that the Spirit is not something, but someone; fully God, not an emanation or aura coming from God. As part of the trinity, the Spirit participates in all the activities of the Godhead For example, when the world was created,
“… the Spirit of God was hovering over the waters.” Genesis 1:2
When Jesus was baptized:
“…the Holy Spirit descended on him, in bodily form like a dove.” Luke 23:22
Jesus promises that after his crucifixion:
“… the Holy Spirit, whom the Father will send in my name, will teach you all things and will remind you of everything that I have said to you.” John 14:26
It is common to think of the Father as the Creator, the Son as Redeemer and the Spirit as Comforter. However, when we assign certain duties to each person of the trinity, we are actually engaging in a heresy know as modalism (big word for the day). They are all involved in each of these important things. One way to think about this is to say that the Father works through the Son by the work of the Holy Spirit.
In addition, within the trinity there is complete accord and unity. The Father loves the Son, the Son loves the Spirit, the Spirit loves the Father, and so on. They are distinct, yet the same. One example given is three separate drops of water, which when held in the hollow of the hand, can be merged together into one. Another analogy is water, steam and ice, the same chemical makeup in different forms. Of course, neither of these is completely accurate, because at the core, the trinity is a mystery that we humans cannot completely grasp or understand.
For more on the trinity, see these posts: