What is the best way to quit during the probationary period?

Unfortunately, I'm currently in a job I don't like at all (I'm still in my probationary period and really haven't been there long xD). Because I was so unhappy, I sent out an application on Monday, got a call the very next day, and the interview was scheduled for today. They said I was the top candidate, and the trial period is next week (which is exactly what I want to do).

Of course, I'll be happy and resign once I've secured the other employment contract. But how does the termination process work? I submit it to my employer in writing, and from that point on, I'm still employed there for two weeks? Or can it be done differently?