Every time we sin, we hurt ourselves, other people and God. The Sacrament of Reconciliation was given to us by Christ to help us reconcile with Christ and His Church.  Through the Sacrament, we acknowledge our sins, express our sorrow in a meaningful way, receive the forgiveness of Christ and his Church, make reparation for what we have done and resolve to do better in the future.
The rite for the Sacrament of Reconciliation involves four parts: contrition, confession, penance and absolution.

• Contrition: a sincere sorrow for having offended God and the most important act of the penitent. There can be no forgiveness of sin if we do not have sorrow and a firm resolve not to repeat our sin.

• Confession: confronting our sins in a profound way to God by speaking about them —aloud— to the priest.

• Penance: an important part of our healing is the “penance” the priest imposes in reparation for our sins.

• Absolution: the priest speaks the words by which “God, the Father of Mercies” reconciles a sinner to Himself through the merits of the Cross. 

A priest can never reveal what he is told in a confession. This obligation of absolute confidentiality and secrecy is most serious. In fact, a priest who violates the Seal of Confession is punished with automatic excommunication.  

If you would prefer to receive the Sacrament anonymously, it's fine. Most confessionals or reconciliation rooms have a screen behind which you can kneel during your confession if you prefer.
 
Won't the priest remember what I said? I'm embarrassed/don't want him to think badly of me.
The priest's purpose is not to keep a check-list on people, but to be an instrument of Christ in receiving someone's sorrow, bringing forgiveness and helping the people move forward. A priest hears a large number of confessions. He is not there to judge the person, but rather the nature of the sin, and to offer counsel and encouragement to overcome the sin and to grow spiritually. He too goes to confession, so he knows how it feels to confront one's own sins and ask for forgiveness. 

The priest may ask for additional information simply to clarify what happened, to understand if the action you confessed was a one-time situation or a pattern, and to assess the person's understanding of the situation. 

Canon #989 says that Catholics are obliged to confess any grave (or mortal) sins at least once a year. That said, parishioners are encouraged to take advantage of the Sacrament at least monthly.  This practice helps us keep aware of our spiritual progress and provides the grace to overcome our sins.   

Any of these is fine. The Rite itself uses Penance and Reconciliation. The Catechism of the Catholic Church notes the sacrament is known by many names:

• “…the sacrament of conversion because it makes sacramentally present Jesus' call to conversion, the first step in returning to the Father from whom one has strayed by sin.

• “…the Sacrament of Penance, since it consecrates the Christian sinner's personal and ecclesial steps of conversion, penance and satisfaction.

• “…the Sacrament of Confession, since the disclosure or confession of sins to a priest is an essential element of this sacrament. In a profound sense it is also a confession'—acknowledgment and praise—of the holiness of God and of his mercy toward sinful man.

• “…the sacrament of forgiveness, since by the priest's sacramental absolution God grants the penitent ‘pardon and peace.'

• “…the Sacrament of Reconciliation, because it imparts to the sinner the love of God who reconciles: ‘Be reconciled to God.' He who lives by God's merciful love is ready to respond to the Lord's call: ‘Go; first be reconciled to your brother.'” (Catechism 1423-1424)

If you are civilly divorced and have not remarried or were validly married after receiving a declaration of nullity for your prior marriage, you may participate in the Sacrament. If you have remarried outside of the Church or have questions about your situation, we encourage you to speak with your parish priest, and to read this online information.  

Another excellent resource is a brochure published by Our Sunday Visitor, called "What the Church Teaches: Annulments," available in the literature racks of many churches. (Our Sunday Visitor)