ANSWER: The answer to your question concerning to whom we should pray requires a somewhat complex answer because we must first understand how the term 'Holy Spirit' is used in the Bible. This requires putting aside what church denominations teach about the subject and let the scriptures guide our understanding with logic and common sense.
If you are like most Christians today, you have been taught that the Holy Spirit is the co-equal third part of the Godhead referred to as the Trinity. The Trinity teaches (with some variations among churches) that God is actually composed of three distinct persons or personalities referred to as God, the Father; God, the Son (Jesus); and God, the Holy Spirit (or 'Ghost' as some translations put it). The Council of Nicaea endorsed this doctrine in 325 A.D. It is still taught by Catholics and Protestants alike. This false doctrine is so pervasive that it is hard to do research on the subject since it is so ubiquitous and assumed to be true.
It is an absolute FACT that the Bible nowhere teaches the Holy Spirit is a 'person.' The Greek translators of the New Testament (most of whom believed in the Trinity) often use the masculine pronoun 'he' when referring to actions God performs utilizing his power. Scholars of the Greek language point out that it is the translators understanding of the reference (or antecedent of the pronoun) that determines whether the masculine (he), feminine (she) or neuter (it) pronoun should be used to make English understandable. Using 'he' is arbitrary; they could as well used 'it' and would have produced a better translation.
The Bible simply does not teach that there is a third member of the Godhead. This fact is even recognized by Catholic Church and Trinitarian theologians!
"The New Testament begins the work, but does not finish it; for it contains no similar teaching (like John 1:1-18 concerning the divinity of Christ) with regard to the Holy Spirit. The unique nature and mission of Christ are traced to a ground in the being of God; but similar ground for the divineness of the Spirit is NOWHERE SHOWN." (An Outline of Christian Theology, W.N. Clark, page 168).
"In Scripture there is as yet no single term by which the Three Divine Persons are denoted together. The word trias (of which the Latin trinitas is a translation) is first found in Theophilus of Antioch about A.D. 180." (Catholic Encyclopedia, Volume XV, 1912)
The Bible teaches two distinct 'persons' who are called 'God': God, the Father, and God, the Son (Jesus). The most succinct statement of this relationship is found in the opening of the Gospel of John.
1. In the beginning was the Word, and the Word was with God, and the Word was God. 2. He was in the beginning with God. 3. All things came into being through Him, and not even one thing that was created came into being without Him.
14. And the Word became flesh, and tabernacled among us (and we ourselves beheld His glory, the glory as of the only begotten with the Father), full of grace and truth. (John 1:1 - 3, 14, HBFV throughout unless stated)
What is it?
What then IS the Spirit? The Apostle Paul wrote to the church in Rome the following.
10. But if Christ be within you, the body is indeed dead because of sin; however, the Spirit is life because of righteousness. 11. Now if the Spirit of Him Who raised Jesus from the dead is dwelling within you, He Who raised Christ from the dead will also quicken your mortal bodies because of His Spirit that dwells within you (Romans 8:6–11)
Here we see the source of the Spirit – it emanates from the Father and Son and is the expression of their power. It was this power that the Father used to raise Jesus from the dead (verse 11). This same power lives in true Christians and enables them to not only change their lives and overcome human nature (verse 7) but also to obey God. This power was used to impregnate Mary with the child that was born as Jesus (Matthew 1:18-21, etc.). It is this power of God that allows us to be 'begotten' as his children and that will eventually allow us to be 'born again' as immortal members of his family (Romans 8:15-17, 28-29, see also 1Corinthians 15).
Finally, consider this quote from our Lord and Savior.
'But I am telling you the truth. It is profitable for you that I go away because if I do not go away, the Comforter will not come to you. However, if I go, I will send IT (not 'him') to you' (John 16:7)
Why would Jesus say that unless He went away, the Comforter (Holy Spirit) would not come to them? It was because he needed to fully complete His mission on earth, be resurrected to God's right hand (Mark 16:19, Acts 2:33, etc.) and given 'all power in heaven and in earth' (Matthew 28:18) before he could send it.
Since the Holy Spirit is NOT a person or Being in some triune Godhead, we should not pray to or worship it but devote ourselves to God alone.