I would describe the steps in the process of a conversion like this:
At some point in a child’s life, he will become aware that he has done wrong, and he will feel guilt and shame. He will probably try to hide his sin from his parents, he may lie to evade accountability. But at that point, he has become morally aware. His conscience has awakened. He is confronted with his need for forgiveness. For Christian parents, this would be a golden “teaching moment”.
As the child grows and asks his endless “why” questions, he will be exposed to creation, and in most homes, he will be instructed about God. He is beginning to make connections between his moral accountability and his Creator.
In a Christian home, the child will be exposed to the stories that explain how Christ has paid for his sins and how he can come to Christ for forgiveness and be changed on the inside. Most people who come to Christ do so during their childhood years.
But even those who come by stranger paths must first become morally aware, and must recognize their accountability to their Creator. And there is only so much that creation can reveal about God. At some point, there must be a revelation of the gospel - how shall they hear without a preacher?
Moral awareness…“God” awareness…gospel awareness…
But being aware of these truths is not enough. The Holy Spirit must convince the sinner of his need to repent and place his trust in the death of Christ to pay for his sins and the resurrection of Christ to raise him to new life. And as the Spirit draws him, as the sinner yields his will to God’s, then he is justified before God in a moment of Spiritual conversion:
a) the old man he used to be on the inside is crucified with Christ,
b) a new man is raised up within him (or born within him - the Bible uses both expressions),
c) this indwelling Spirit interconnects him in a Spiritual union with all other saints across the ages and around the world (the Bible describes this as being baptized by the Spirit into the Body of Christ),
d) he becomes an immediate heir to a glorious future - this is the actual point of adoption.
As His life proceeds, he will experience a lifelong process of sanctification whereby the indwelling Spirit conforms him by increasing degrees into the likeness of Christ.
And this process will be consummated when he leaves this world and stands perfect before his Savior in the afterlife.
Moral awareness…“God” awareness…gospel awareness…Spiritual conviction…justification by faith… sanctification throughout life…glorification in eternity.
I will admit that I have simplified this greatly, so if you have any more specific questions about certain steps in this process, let me know and I will try to answer as best I can.