I'd like to ask you righteous and knowledgeable gentlemen about the concept Teshuvah. Is there a determined ritual for "completing" it? Is it just a state of mind? When does one know it has been effective? I thank you immensely for you information.

The Rambam mentions three steps in the process of Teshuva. The first is to have regret over his sin.The next step is to confess his sin.The third step is to accept upon himself never to do the sin again.
The real sign that a person has done an effective teshuvah is when he is presented with the same opportunity to sin and refrains from it.

Who must he confess the sin to?

He must confess to God

Thanks a lot, I feel I may be getting somewhere..

I had a question what was the purpose of confession. The "leaving the sin" was simple, if you are still sinning , how can you repent? . Accepting not to do it in the future is also understandable, since if you are going to turn around and sin, what use is repenting? But what does confessing do?

The I think is, that when someone does something wrong, he rationalise it, saying it's realy not so bad, maybe on a small scale he did something not proper, so to cover all bases he'll repent for "maybe" he did something with the smallest amount of badness. So therefore you need to confess, to say that you sinned completely, without excuses. Because if you have excuses, and what you did was basicaly good, why should there be any change, then the other 2 parts of repentance wouldn't have any meaning

I think also that saying vidui out loud is like saying the bracha out loud. It actually brings the thought into the physical world and gives it a reality it does not have when unexpressed. The fact that we give expresions of our souls reality by bringing them out has profound spiritual effects on the world.