Where does it say that the Holy Spirit is God?
"But Peter said, "Ananias, why has Satan filled your heart to lie to the Holy Spirit and keep back part of the price of the land for yourself? While it remained, was it not your own? And after it was sold, was it not in your own control? Why have you conceived this thing in your heart? You have not lied to men but to God." ... Then Peter said to her, "How is it that you have agreed together to test the Spirit of the Lord? Look, the feet of those who have buried your husband are at the door, and they will carry you out."" (Acts 5:3-4, 9). Notice that Peter used the terms "Holy Spirit" and "God" interchangeably. He perceived the Spirit to be God.
Such should not surprise the student of the Bible. The Holy Spirit is describes as possessing characteristics which are unique to God. He is omniscient, that is He knows all things. "But God has revealed them to us through His Spirit. For the Spirit searches all things, yes, the deep things of God. For what man knows the things of a man except the spirit of the man which is in him? Even so no one knows the things of God except the Spirit of God" (I Corinthians 2:10-11). The Spirit is also omnipresent, that is He is everywhere. "Where can I go from Your Spirit? Or where can I flee from Your presence? If I ascend into heaven, You are there; If I make my bed in hell, behold, You are there. If I take the wings of the morning, And dwell in the uttermost parts of the sea, Even there Your hand shall lead me, And Your right hand shall hold me" (Psalm 139:7-10). The Spirit of the Lord is also eternal. "How much more shall the blood of Christ, who through the eternal Spirit offered Himself without spot to God, cleanse your conscience from dead works to serve the living God?" (Hebrews 9:14).
We also find the deity of the Spirit demonstrated in His workings. He was involved in the creation of the world. "The earth was without form, and void; and darkness was on the face of the deep. And the Spirit of God was hovering over the face of the waters" (Genesis 1:2). Or, "The Spirit of God has made me, and the breath of the Almighty gives me life" (Job 33:4). It was through the Spirit that miracles occurred. "But if I cast out demons by the Spirit of God, surely the kingdom of God has come upon you" (Matthew 12:28). And, "For I will not dare to speak of any of those things which Christ has not accomplished through me, in word and deed, to make the Gentiles obedient -- in mighty signs and wonders, by the power of the Spirit of God, so that from Jerusalem and round about to Illyricum I have fully preached the gospel of Christ" (Romans 15:18-19).
The Spirit had a hand in the redemption of man. "How much more shall the blood of Christ, who through the eternal Spirit offered Himself without spot to God, cleanse your conscience from dead works to serve the living God?" (Hebrews 9:14). Notice that the Son, the Spirit, and the Father are all mentioned in this one verse working together to bring about the redemption of man. Yet, each are listed independently. See Subtle References to the Trinity of God for other similar cases in the Scriptures.
Finally, the Spirit is involved in the regeneration of man. "Jesus answered, "Most assuredly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God."" (John 3:5). And, "But when the kindness and the love of God our Savior toward man appeared, not by works of righteousness which we have done, but according to His mercy He saved us, through the washing of regeneration and renewing of the Holy Spirit, whom He poured out on us abundantly through Jesus Christ our Savior, that having been justified by His grace we should become heirs according to the hope of eternal life" (Titus 3:4-7). Once again notice in this last passage that the Father, the Spirit, and the Son are all mentioned working together for the salvation of men.