I was caught blatantly cheating once in middle school. The teacher met with me and my parents, and I really had no way to deny it. I mean, it was flagrant. My parents hit the roof.
My school said they would put a note in my file, and as long as there were no more incidents they would throw away the note and it wouldn't be part of any permanent record. The whole incident left a pretty big impression on me at the time. I can't recall cheating in high school for my own gain, although I did allow friends to copy homework assignments from me. Simple worksheets, not essays or projects.
Now I'm a teacher, and I've had to handle the issue of plagiarism from a published source or website a number of times. My first step is always a conversation with the student. At the age level I deal with (middle school) they don't always fully understand the issue. If that doesn't do it, then I move to discussing it with the parents.
In the case of copying from peers I usually move more quickly to contacting the parents.