Repentance with Godly sorrow and repentance with a worldly sorrow
True Repentance--the only kind that will ultimately matter--is a gift of God. Both true faith and true repentance exist in the heart that has been regenerated by the power of the Holy Spirit. This regeneration is what Jesus spoke of when He said, "except a man be born again, he cannot see..." It is as the Holy Spirit miraculously gives them birth that they see, truly repent, and truly believe. Repentance, therefore, is more a gift that God gives rather than a ritual that men perform.
That you ask such a question, however, indicates that God has placed you in the way--on a path--which ultimately will issue in that gift being given you. The God and Father of our Lord Jesus Christ is the God of all grace and the Father of mercies. Therefore seek these gifts earnestly from Him and do not be content with performing some ritual men may require of you. Pray as the psalmist prayed, "Why have you hardened our hearts from your fear? Turn us again, oh God. Turn us and we shall be turned." Repentance is at times expressed as a turning about. It is a change of mind which brings a person's mind into agreement with God, turning him/her from rebellion against God to agreement with and love of God.
The Holy Spirit uses the preaching of the gospel and His word as tools in performing His work of regeneration. Therefore, diligently seek to sit before ministers who are faithful in preaching the excellencies of Christ and the riches of His grace, and carefully read the scriptures, especially the gospels, with an awareness that the things you see in the Lord Jesus are also the things that can be seen in the Father because Jesus is exactly like the Father is. Do you see compassion in Jesus when you notice that He never turned anyone away who came to Him in need? Well, the Father is that way also. Do you see forgiveness in Jesus when He says to people time after time, "thy sins be forgiven thee"? Well, the Father is also forgiving.
As you sit before the preached word and as you read it, remember with every word that Jesus came to "call sinners; "to seek and to save that which was lost;" remember that He came "not to call the righteous [that is, those who considered themselves okay] but sinners to repentance."
Placing trust in Jesus is the same as having faith in Him. It is as we learn of Him that we come to trust Him because He is ALTOGETHER WORTHY of our placing our confidence in Him. Who else could we rely upon? Our only other choice is to hope that we in ourselves are good enough for God; but NONE OF US MEET THE STANDARD GOD REQUIRES. Only Jesus has met that standard, but when we realize that there is salvation in and through Him, when we understand that He clothes those who cast all their hope in Him, clothing them with HIS OWN RIGHTEOUSNESS, we begin to truly turn away from rebellion against Him. We begin to cast ourselves upon Him, casting away all hope in any SUPPOSED righteousness of our own (for none of us have ANY).