As a husband or wife have a role and function in their marriage, in much the same way the Holy Spirit has a special role and function in the Godhead.  In connection with the Holy Spirit’s role, I think it is essential, first of all, to understand that the Holy Spirit proceeds from the Father and the Son.  In John 15:26 Jesus explains the Holy Spirit as one who proceeds from the Father.  And I think the Holy Spirit also proceeds from the Son since the Father and the Son are one.  This word “proceed” means to flow from.  That does not mean that He came from the Father and the Son as to originate from them or to be generated from them; but rather, proceed means that He eternally flows from the Father and the Son as to extend or to advance their life and purpose. Also, I think this proceeding of the Holy Spirit means that He has been, is, and always will be the spirit of the Father and the Son.             

I think we have a good illustration of this proceeding in Revelation 22:1.  Here one of God’s angels gives John a glimpse into heaven, showing him a river “proceeding” (or Flowing) from the throne of God and of the Lamb.  This river is described as “a pure river of water of life, clear as crystal.”  Well, though this river I believe may be an actual river in heaven, it is clear to me that it represents the Holy Spirit.   Why do I say this? Because in John 7:37-39 Jesus talks about the “rivers of living water,” and in verse 39 He explained it as the Holy Spirit.  John was the author of both the Gospel of John and Revelation. Therefore, when he spoke of the river of living water in John as being the Holy Spirit I think we can also understand the river of life in Revelations 22:1 to also mean (or represent) the Holy Spirit.  The Lamb of God in Revelations 22:1 is of course Jesus, and the One on the throne of God is of course God the Father.  Therefore, I see this river of life in Revelation as the Holy Spirit proceeding from the Father and the Son. It is a picture of the trinity at work.           

The role of the Holy Spirit in our life is that He brings the spirit of the Father and the Son to us, and is the life of the Father and Son in us.  He brings their spirit to life in us, and so energizes our spirit for prayer and good works.  In other words, the Holy Spirit works in our spirit the life and purpose of the Father and the Son.  Thus, whatever He sees the Father and Son doing, He conveys that to us (in our spirit). 

Moreover, as the Holy Spirit works in us, we get the sense of the working and thinking of the Father and the Son, because, in fact, mystically, the Holy Spirit is the spirit of the Father and the Son, though He is His own person and operates His ministry “in His own power.” 

Now in terms of prayer, here are the roles of the Godhead:  

The Father is the source of what we pray for—all prayer comes from the Father.

Christ is the channel for our prayers—all prayer must go through Christ.  He makes our prayers holy by His blood; thus they are acceptable to God.  

The Holy Spirit is the agent of our prayers.  He is the one that moves our prayers by His power back to the Father through Christ.

But the Holy Spirit is not just a carrier of our prayers.  He does more than that.  He brings our prayers along and helps us in our praying from start to finish.  Here are four things that He does:  (1) He gives us a desire to pray—or we could say that He conveys the desire of the Father and the Son to us; (2) He inspires our prayers; (3) He helps us pray; and (4) He brings our prayers to the Father and makes them acceptable through Christ.  

Thus, as we can see, the Holy Spirit is the enabling agent all along the way.  He does the work of prayer in us.  But let me be quick to add that His purpose is not to exalt Himself, but rather to lift up the person of Christ, who in turn glorifies the Father.  

This is the way I believe it works: 

The Father is the head and source of all things. 

The Son is the brightness and the glory of the Father (Jn. 1:14). 

The Holy Spirit conveys to us (by His spirit to ours) the glory of the Father and the Son, and works to bring us into their glory and fellowship.