This lesson is about repentance from sin and the attitudes and actions that accompany it and make it genuine.
Godly sorrow
The scriptures tell us that "godly sorrow produces repentance" (2Co 7:10). Repentance requires that we feel remorse, and truly sorry for the sins we have done. Of course, we can have a sorrow for sin and still lack repentance. The rich man who "went away sorrowful" (Mtt 19:16-22) is an example. We may feel sorry about being condemned for sin, yet still not want to let that sin go. So there can be sorrow for sin without repentance, but there cannot be repentance without a genuine godly sorrow.
Guilty conscience
Peter's preaching caused many people to be "cut to the heart" and to cry out "What shall we do?" (Acts 2:37). Peter then told them to repent and be baptized (Acts 2:38). Their conviction of sin led them to repentance. Of course, one can have a guilty conscience without repentance. For example, Judas who betrayed Jesus had a guilty conscience, but he committed suicide instead of repenting unto life (Mtt 27:3-5). So there can be a guilty conscience without repentance, but there cannot be repentance without a genuine conviction of guilt.
Confessing sin
Not only should we feel the conviction of sin, but we should be willing to acknowledge the sin to God. Of course people can acknowledge sin without repentance. We have all heard people boast about their evil deeds. We also know that on Judgment Day every one must give account to God (Rom 14:10-12). In the case of those who have sinned and not been forgiven, their account to God must necessarily entail a confession of sin. However they will have no more opportunity to repent. So there can be a confession of sin without repentance, but there can be no repentance without confessing sin.
Asking forgiveness
Not only must we acknowledge sin, but also be willing to ask forgiveness. Jesus taught us to pray, "Forgive us our sins..." (Mtt 6:12). Peter told Simon the sorcerer to repent and pray for forgiveness (Acts 8:22). Of course one can request forgiveness and still lack repentance. The unmerciful slave asked forgiveness, yet he obviously had not repented (Mtt 18:23-35). So one can ask forgiveness without having repentance, but one cannot have repentance without going on to ask forgiveness.
Making amends
An important part of repentance is the willingness to make restitution where possible. Of course one can make amends without having repentance. The courts might force a graffiti vandal to clean off the paint, but the vandal may not have repented. Also, the act of making amends is not itself repentance. Zacchaeus, for example, had already repented of sins, and salvation had already come to him, but he had not yet actually made the amends that he had promised. Nevertheless the genuine intention to right his wrongs was necessary to the repentance that saved Zacchaeus (Lke 19:8-9).
John the Baptizer told the Pharisees, "Bring forth fruits in keeping with your repentance" (Mtt 3:7-8). Peter said, "Repent and be converted that your sins may be blotted out" (Acts 3:19). So we should not think of repentance as a loopehole for dodging responsibility for the consequences of our wrongdoings. Rather, repentance includes a commitment to a changed way of life which includes trying to undo and make up for the wrongs we have done.
Change of intention
All the other things we have discussed ought to go along with repentance. These things are not genuine unless accompanied by repentance, and there cannot be any genuine repentance if not accompanied by these things. But what is repentance itself? Repentance is giving up the intention to do evil, and deciding to do the will of God.
Note that repentance is "toward God" (Acts 26:20). Also note that the Greek for repentance is metanoia meaning a change (meta) of mind (nous). So we see repentance to be a change of intention such that one no longer intends to do evil, but intents to do God's will.