Penance was instituted by Christ after the resurrection when he breathed on the disciples and said: "Receive the Holy Spirit. If you forgive the sins of any, they are forgiven; if you retain the sins of any, they are retained" (John 20:23).  Matthew 16:15-20 also mentions a similar theme where Jesus gives Peter the keys and the authority to bind and loose.  The book of James gives witness to the early form of public confession, as well as to its healing power (James 5:13-18).

In the early Church, confession and penance were very public affairs.  A person, after committing a grave sin, would ask the bishop for penance and would publicly live the life of a penitent (in an order of penitents), meaning exclusion from communion, as well as a strict course of prayer, fasting, and almsgiving.  After this period, sometimes lasting years, the person was forgiven and allowed to return to normal Christian life.  However, there were limitations.  For example, this could only be done once in a lifetime.  This system had obvious drawbacks, especially when more and more people became baptized after Christianity became legal under Constantine.

A new way of celebrating this Sacrament came to us from the Celtic (or possibly Anglo-Saxon) peoples.  The monks of the British Isles had a system that lacked both an order of penitents and the requirement of only one penance in a lifetime.  They also allowed the sin itself to be kept secret.  However, like the methods of the continental and Eastern Church, penance was still public, long, and absolution came only at the end.  At some point, confessors started issuing absolution in advance, that is, before the penance was fulfilled.  Thus, at this point, we have the beginnings of the current celebration of the Sacrament: confession, absolution, and then doing the penance.

Formally, the Fourth Lateran Council (1215) enjoined this method of confession and made it mandatory for Catholics to do at least once a year.  The councils of Florence (1431-1439) and Trent (1545-1463) more precisely defined the nature of Reconciliation, even though the practice goes back to the earliest days of the Church and Jesus himself.  The emphasis of the Sacrament was expanded with the Second Vatican Council, which emphasized reconciliation and amendment of life and allowed the option of public services of penance (but these must always include auricular (meaning private) confession).  However, the basic theology behind the Sacrament has remained the same, namely reconciliation with God.

The Catholic Church teaches the primary elements of the Sacrament are 1) contrition, 2) confession, 3) absolution and 4) satisfaction. The sinner confesses his sins and vocalizes his internal repentance.  The priest then gives penance and through the power of his ordination, pronounces the words of absolution. 

After the confession, the person will make an "act of contrition" which is an outward prayer in front of the priest that affirms the person's inward state of being sorry.  Then the priest will give counsel and assign a penance.  Finally, the priest says the words of absolution and we are forgiven, a cause of great rejoicing!  The priest is not the source of forgiveness, God is.  However, the priest, ordained in valid apostolic succession, acts as God's ambassador, and is the instrument God has chosen to use by which he forgives our sins.  The absolution remits the guilt and the eternal punishment of mortal sin.  So, why does the priest assign us penance and why is this necessary?

When we sin, we offend God and his justice.  An offense against justice requires some kind of satisfaction.  It's like when a person steals, even if he is completely forgiven, justice requires him to make reparation.  The Bible is full of examples of temporal punishment for sin: Adam and Eve, David, Solomon, etc.  Penance, then, is our way of making reparation for our sins.  This is not earning our salvation since we are not in danger of hell after the absolution.  It is simply making reparation to God for our wrongs we have done.  The Catholic Church does not burden people with excessive penances and the priest usually assigns a few prayers or an act of charity.  The early Church, as noted above, strongly believed in the concept of penance.   The Catholic Catechism explains penance well: Many sins wrong our neighbor. One must do what is possible in order to repair the harm (e.g., return stolen goods, restore the reputation of someone slandered, pay compensation for injuries). Simple justice requires as much. But sin also injures and weakens the sinner himself, as well as his relationships with God and neighbor. Absolution takes away sin, but it does not remedy all the disorders sin has caused. Raised up from sin, the sinner must still recover his full spiritual health by doing something more to make amends for the sin: he must "make satisfaction for" or "expiate" his sins. This satisfaction is also called "penance" (#1459).

1. A person begins with a good examination of conscience. We need to hold up our life to the pattern of life God has revealed for us to live. For instance, we take time to reflect on the 10 Commandments, the Beatitudes, the precepts of the Church, and the virtues of prudence, fortitude, temperance, and justice.  The examination of our conscience is like stepping back and looking at the picture of our life in comparison to the masterpiece of life revealed by God.  In examining our consciences, we step back and honestly assess how well we fit God’s pattern and have stayed within His boundaries.  We also reflect on the progress we have made since our last confession in dealing with weaknesses, faults, temptations, and past sins.  We must recognize the venial sins — those lighter sins which weaken our relationship with the Lord — from the mortal sins — those sins which sever our relationship with the Lord and “kill” the presence of sanctifying grace in our souls.  Here we remember the words of Jesus, “Everyone who practices evil hates the light; he does not come near it for fear his deeds will be exposed. But he who acts in truth comes into the light, to make clear that his deeds are done in God” (Jn 3:20-21).
2. Given this examination of conscience, we have contrition for our sins.  While we are sorry for sin because we do fear the fires of Hell and the loss of Heaven, and the just punishments of God, we are sorry most of all because our sins offend God whom we should love above all things.  The love for God moves us to repent of sin and seek reconciliation.  All of the great saints regularly examined their consciences and made frequent use of the Sacrament of Penance. 
3. Sorrow for sin moves us to have a firm amendment not to sin again.  We probably will sin again, but we try not to do so.  We do not plan on leaving the confessional and committing the same sins again.
4. We then confess our sins.  When we enter the confessional in most Churches, we have the option of remaining anonymous or facing the priest.  Whichever option a person chooses, always remember that whatever is said during the confession is held in secret by the priest.  Remember also that we confess to the priest for three reasons: First, the priest has the authority of the apostles by virtue of his ordination. On the night of the resurrection, Jesus said, “Receive the Holy Spirit. If you forgive men’s sins, they are forgiven them; if you hold them bound, they are held bound” (Jn 20:22-23). The priest is the minister of the sacrament acting in the person of Christ.  Second, he is the spiritual father. Just as we see a doctor for healing when we are physically sick, we see a priest when our soul is sick and needs healing.  Third, the priest represents the Church and the people we have sinned against. In the early days of the Church, people publicly confessed sin at the beginning of Mass and were absolved. Much to our relief, for centuries now we have had private confession.
5. We proceed by making the sign of the cross and saying, “Bless me father for I have sinned.”  One could also simply begin, “In the name of the Father....”  We should then state when we made our last confession: “It has been (so long) since my last confession.”  
6. We then confess our sins. We must be specific. Sometimes people say, “I broke the sixth commandment,” which covers everything from a lustful thought to rape and adultery. We do not need to provide details, just the basics to enable the priest to help.  We need to give some quantification — missing Mass once is different from several times which is different from all the time.  When we are finished confessing our sins, we state, “I am sorry for these and all of my sins.”  With this information, the priest may counsel us.  He also assigns a penance for the healing of the hurt caused by sin and the strengthening of our soul against future temptation.  He then asks us to say an Act of Contrition, which is generally the traditional prayer: “Oh God, I am sorry for my sins with all my heart.  In choosing to do wrong and failing to do good, I have sinned against You Whom I should love above all things.  I firmly intend, with the help of Your grace, to do penance, to sin no more, and to avoid the near occasion of sin. Amen.”
7. Finally, the priest imparts absolution, “God the Father of mercies, through the death and resurrection of His son, has reconciled the world to Himself and sent the Holy Spirit among us for the forgiveness of sins; through the ministry of the Church may God give you pardon and peace, and I absolve you from your sins, in the name of the Father, and of the Son, and of the Holy Spirit.” This formula emphasizes our merciful Heavenly Father, the saving mystery of our Lord’s passion, death, and resurrection, and the healing ministry of the Holy Spirit through the Church.
8. The priest then dismisses us and we then leave the confessional to do the assigned penance.