As I said in my first post, different countries could certainly have different polacies. In Tim's story, Für Das Größere Wohl, Muggle-borns receive their letter exactly on the their eleventh birthdays (Godric help the student who was born on August 31st.).
And in my own stories, students in the United States get their letters two years in advanced, while students in Australia get their letter a year before they would be set to go to school.
I was actually just reading on this very subject a few days ago, as I am in the process of deciding on a future career for my OC. In the list of careers I discovered (I will provide the site later; I'm not at my personal computer right now.), there was a Muggle Relations Committee within the Ministry of Magic. Each Liason on this committee worked with the relationships between Muggles and Wizards - including helping in the transition for witches/wizards born into Muggle families. I think it is the people in this particular department that take care of explaining things to the Muggles - at least as far as this site is concerned. I think it was Lexicon, but I'll have to double check.
There's a mention of a Muggle liaison office on the HP Wiki, located in the Department of Magical Accidents and Catastrophes in the Ministry of Magic.
It would make sense that a professional would handle the situation. But I could also see a teacher going, so I think it really depends on what the author wants to do.