We are introduced to the Holy Spirit in the book of Genesis, chapter 1:2, at the very beginning of the Bible. The Holy Spirit is there hovering over the waters of the Earth. IN Genesis, it appears that God is connecting the Holy Spirit with the creation of life, as we know it. Later on, after Jesus rises from the dead, he sends the Holy Spirit into the inner being of those who choose to accept God's invitation to be saved from the corruption and decay of this world through Christ, adopted by God and born-again. There, inside a follower of Christ, the Holy Spirit is again involved with creation - the re-creation of believers. The Holy Spirit transforms broken, disconnected people into whole people who are re-connected with God and empowered to function as His sons and daughters who reflect His true image.
In the beginning God created the heavens and the earth. Now the earth was formless and empty, darkness covered the surface of the watery depths, and the Spirit of God was hovering over the surface of the waters. Genesis 1:1-2
Throughout the bible, the Holy Spirit is referred to as the "Spirit", the "Spirit of God", the "Spirit of Jesus". Another way of understanding these last two terms is "Spirit belonging to God" and "Spirit belonging to Jesus". Although the word "trinity" is not in the bible, it is clear that God, Jesus and the Holy Spirit truly do function in community with one another. They belong to one another. Yet, they each have a unique purpose and personality. This is still a mystery. Some have explained this concept as that of the different states of water: solid (ice), liquid (water), steam (air). Thus, they are all "water" but in different environments. They are used for different reasons and serve different purposes.
Interesting Observation: God connects and compares the Holy Spirit to water, air (His breath), light and life throughout all of the Bible. In fact, the words for God's Spirit and God's Breath are used interchangeable throughout the Old Testament. God uses our understanding of these things and their properties to explain the workings of the Holy Spirit. God is the best teacher and truly wants us to understand our environment, as much as is possible with our current brains.
For by one Spirit we were all baptized into one body, whether Jews or Greeks, whether slaves or free, and we were all made to drink of one Spirit." 1 Corinthians 12:13
"The Spirit of God has made me, And the breath of the Almighty gives me life. Job 33:4
You send forth Your Spirit, they are created; And You renew the face of the ground. Psalm 104:30
"It is the Spirit who gives life; the flesh profits nothing; the words that I have spoken to you are spirit and are life. John 6:33
The Hebrew word for the Holy Spirit is the "Blessed Ruach". It is interesting to note that the gender of the Holy Spirit (the Blessed Ruach) all throughout the Old Testament is female. In the New Testament, it is masculine. In the Book of Job it is inferred that the Spirit is the "womb of the earth" where God's seeds (which only He can plant) will thrive, grow, and reproduce. Thus, as described above, the Spirit sets forth an "environment" through which God's good purposes and seeds of life can flourish and grow. The Spirit is likened to a healthy womb. Some might even say the Holy Spirit is a catalyst through which God does his work. I recommend studying out the concepts of "sowing in the Spirit" vs. "sowing in the flesh" in the Bible.
From whose womb comes the ice? Who gives birth to the frost from the heavens Job 38:29
And they (the believers) will be called oaks of righteousness, a planting of the Lord, to illuminate Him (his true essence) Isaiah 61:3
For as a garden enables what is sown to spring up, so the Lord God will cause righteousness and praise to spring up before all nations. Isaiah 61:11
Note: A garden and a womb are both environments that can promote reproduction and life.
Here's an interesting blog entry from someone I do not know personally. It reframed Genesis 1:1-3 in a very interesting way: The Security of the Womb
Jesus described the Holy Spirit as our Counselor, Comforter, Nurturer, Teacher, Illuminator. All throughout the gospel of John, chapters 14-16 especially, Jesus explains about the Holy Spirit, whom he will send to inhabit his followers. I encourage you to read these chapters slowly and absorb their rich teaching.
"If you love Me, you will treasure my teachings. And I will ask the Father, and He will give you another Counselor to be with you FOREVER. He is the Spirit of truth. The world is unable to receive Him because it doesn't see Him or know Him. But you do know Him, because He remains with you (i.e. in the form of Jesus) and will be in you. I will not leave you as orphans; I am coming to you (in another form)." John 14:15-18 (Note: Items in italics are my opinion and my explanation.)
"But the Helper, the Holy Spirit, whom the Father will send in My name, He will teach you all things, and bring to your remembrance all that I said to you." John 14:26
"When the Helper comes, whom I will send to you from the Father, that is the Spirit of truth who proceeds from the Father, He will testify about Me, and you will testify also, because you have been with Me from the beginning." John 15:26-27
"But when He, the Spirit of truth, comes, He will guide you into all the truth; for He will not speak on His own initiative, but whatever He hears, He will speak; and He will disclose to you what is to come." John 16:13
"He will glorify Me, for He will take of Mine and will disclose it to you." John 16:14
The Holy Spirit is invisible to us right now. Technically, our eyes are limited to only a small subset of light waves. Someday, when we receive our new bodies from God, we will be able to "see" all wavelengths - gamma rays, x-rays, ultra-violet, radio waves, etc. But, right now, we "see" the Holy Spirit by observing the "fruits" of his work.
Here is what the bible talks about as the "fruits" of the Holy Spirit:
"But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, and self-control." Galatians 5:22
More will be added to this study soon.