Hi there! Thanks for your question.
CCC #2487 says this:
Every offense committed against justice and truth entails the duty of reparation, even if its author has been forgiven. When it is impossible publicly to make reparation for a wrong, it must be made secretly. If someone who has suffered harm cannot be directly compensated, he must be given moral satisfaction in the name of charity. This duty of reparation also concerns offenses against another’s reputation. This reparation, moral and sometimes material, must be evaluated in terms of the extent of the damage inflicted. It obliges in conscience.
So the Catechism is clear that public reparation is the general way of dealing with an offense.
In French, reparer simply means to fix. Simply put, we’re called to fix things after committing an offense against someone.
The first thing that comes to my mind is to simply say sorry and ask for forgiveness in front of the person. You tell them, “I’m sorry. Can you forgive me?” and then it’s on them to forgive you. If you did something that hurt them or damaged their property, you should offer to pay the medical bill or mechanic’s bill or contracter’s bill (or replace whatever you broke or damaged). Financial compensation is a good way to make public reparation for a wrong. Another way that comes to mind is to give of your time—your service to that person. If you, say, trampled your neighbour’s rose bushes because you walked outside and were angry, then you could offer to give an hour of your day during the summer helping your neighbour in their garden.
On a more serious note, public reparation could mean serving a jail sentence or paying a severe fine. Pleading guilty and accepting your jail time would be a good way to make public reparation. Remember, once you commit a wrong and you realize it is wrong, it is up to you to “make up for it” as best you can.
I hope I was able to answer your question. Take care!