There is a process for renouncing one's faith. It does not erase your Baptism because it is a historical fact and we Catholics believe that Baptism forever changes you. For example, if you decide to renounce your faith and then some day regret that and come back, we would not Baptize you again, we would accept you back as a family member. Family is a good analogy actually, one could renounce one's family but they are still your family.
So with that in mind, it is a threefold process:
- It has to be evident that it is your choice and no one else's.
- You commit an act of heresy, schism, or apostasy (i.e. join another Church with the thought that you are leaving the Catholic Church, or write a letter that expresses your denial of an essential truth of the faith)
- This must be accepted by a competent authority in the Catholic Church. This would be either your Bishop or your territorial pastor.
Once these three things happen, a note is placed in your Baptism record that says that you renounced your faith.
These notes are written in pencil usually, because, as I said you can come back, when you are ready, to full Communion and we will accept you.