Celebrating Reconciliation occurs generally in these three manners: Saturday Confessions, Seasonal Reconciliation Services or Personal Appointment with a Priest.
The normal structure of the Sacrament begins with the Person initiating it with the Sign of the Cross, and then saying "Bless me Father, I have have sinned. It has been (give a time reference) since my last confession. Here are my sins.
The person then lists the sins that he or she is aware of and can earnestly remember.
The priest will listen, and can advise and provide insight.
The priest will give a penance. A penance is a way for the person to make amends, to be healed and to heal for the sins. It is generally up to the priest to give this. However, the person must be able to complete this penance. Therefore if a penance is received that a person is unable to perform without hardship, another penance can be requested by the person. The penance must be completed in the time give by the priest.
The person then prays the Act of Contrition. This may be a form that we learned, or it may also be a prayer that comes from the heart. It will need to address the Father, express sorrow for the sin, and a recognition that it is through Christ that freedom from sin is experienced.
The priest will then pray the Words of Absolution, and then the person is dismissed.
It is normal to be nervous. Remember though, the priest is sworn to secrecy. The Seal cannot be broken. So whatever is said in the Sacrament, stays there.
If it has been many many years since a person has celebrated the Sacrament of Reconciliation, consider setting up an appointment with the priest. This will provide ample time for any conversation. Generally Saturday confessions or Seasonal Reconciliation Services do not have the time needed to properly give to a long away penitent.
Remember too this is a time of grace and healing. It is not about necessarily feeling horrible about our pasts, but about beginning anew for the future. It is an opportunity to begin again in life.