You can choose to confess anonymously (behind a screen) or face-to-face. The priest will greet you and lead you in the Sign of the Cross. Then you should say, "Bless me, Father, for I have sinned. It has been (approximate days, months, or years) since my last Confession." Then tell the priest all of the sins you are aware of. Try to keep things brief and specific. The priest may ask some questions. When you are finished, conclude with words such as "I am sorry for these and all my sins."
At this point, the priest may give you some advice or encouragement. Confession isn't the place for a full counseling session, so you will want to schedule that separately if necessary. The priest will give you some act of penance to perform. This gives you an opportunity to change your ways, repair the damage caused by your sin, and draw closer to God. It might be prayer or an action, and you should try to do it as soon as you can. Doing your penance doesn't earn you forgiveness (nothing could), but it's good for you!
Next is the Act of Contrition, a prayer of repentance and reform. You can pray a standard version (including the ones in this week's LANE resources) or pray spontaneously.
