Oh my God, I am heartily sorry for having offended Thee, and I detest all my sins because of Thy just punishments; but most of all because they offend Thee, My God, who art all good and deserving of all my love.  I firmly resolve, with the help of Thy grace, to sin no more and to avoid the near occasion of sin.  Amen. 

My 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 your help, to do penance, to sin no more, and to avoid whatever leads me to sin.

Our Savior Jesus Christ suffered and died for us. In his name, my God, have mercy.

O my God, 
I am heartily sorry for having offended Thee, and I detest all my sins, because I dread the loss of heaven, and the pains of hell; but most of all because they offend Thee, my God, Who are all good and deserving of all my love. 

I firmly resolve, with the help of Thy grace, to confess my sins, to do penance, and to amend my life.

Amen.

Then Jesus straightened up and said to her, “Woman, where are they? Has no one condemned you?”

She replied, “No one, sir.” Then Jesus said, “Neither do I condemn you. Go, [and] from now on do not sin any more.”

Before Entering the Confessional

An Examination of Conscience is required for an individual to approach the confessional with a clear understanding of the sins they need to be unburdened of.  This could take the form of simply recalling to mind any grave sin that has taken place since your last confession, or it could go even deeper by reflecting on each of the Ten Commandments and assessing the times you have not followed God's laws.  If you have forgotten any serious sins, these will be covered by absolution.  If you withhold confessing serious sins you are aware of, your absolution will be invalid.  

Entering the Confessional

Once you have opened the door and either knelt or sat behind a screen, or sat face-to-face with the priest, he will greet you with a short exhortation for a good confession.  You will then recite the following:
 

"Bless me Father, for I have sinned.  It's been [amount of time] since my last confession."

It doesn't matter how long you've been away from the confessional - the priest is not there to shame you - let it all hang out!

Making a Good Confession

After you've been greeted and revealed the time elapsed since you were last in the confessional, proceed to confess your sins.  There are different schools of thought on what makes a "good" confession, but it is customary to simply list your sins and the number of times you have committed those sins;  or to list the commandments you've violated, along with the specific sin committed.  It is not necessary whatsoever to provide backstory or context to the priest.  You may elect to do so, but the confessional is first and foremost about admitting sin and being absolved, plain and simple.  

On the other hand, if you are willing to provide some color around your sins, your confessor (the priest) is likely to provide you additional guidance tailored to your circumstance in life.  The priest is open to the Holy Spirit, and is willing to provide counsel if there is something to work with.  Although this is not necessary to the sacrament, it has become commonplace for advice to be offered to the penitent, along with absolution.  The priest may also ask you for addtiional context if he believes he can assist you in overcoming the sin with helpful direction.  

After Confessing

Once you're finished confessing, the priest will give you a penance.   Penance is not intended to be an undue burden, however, it's important for you to know that penance performed after absolution is meritorious, and reduces time owed in purgatory for your sins.  Your penance may be as little as one Hail Mary, or a Scriptural reading, or something specific to your circumstance.  A greater or lesser penance is not indicative of the sins that were absolved.  Sometimes, the Holy Spirit asks the priest to give you something with a little more "meat on the bone" so that you may derive even greater graces from your sacrifice.

The priest will then say to you, "and now make an act of contrition."  At this point you can either say the actual "Act of Contrition" (there are several versions you can choose from), or, it is also acceptable to express your sorrow and willingness to avoid future sin, in your own words.  

Absolution

After you make your act of contrition, the priest will preface absolution with a prayer, followed by the specific words:  "...And I absolve you from your sins, in the name of the Father, and of the Son, and of the Holy Spirit."  The priest *must* use this formula, or absolution does not take place.   He cannot say, "I forgive", or "the Church forgives," or "we absolve", etc.  It's "I absolve you..."   See the FAQ for more details.  

Done!

Congratulations!  You've just been absolved of all your sins!  Don't be a stranger, we all sin, so come back often and you'll be richly rewarded by God!