How do AP classes work?

I have never heard of anyone getting AP credit without the classes but perhaps things have changed since I did AP.

I suspect the Chinese student simply took an exam. If she is fluent in Chinese, she probably didn't have to study much -- language exams tend to be translation or essay writing but not something technical like in the Physics AP.

There are probably prep classes for AP but, at a certain point, why not just go to AP courses as per normal, instead of a prep company?

I'm not completely sure, but if you do not take the class, you will only be given the AP credits for the test. If you get a 3 or higher then colleges usually accept it, but they rarely accept anything lower. There are plenty of ways to study for the test, however. The collegeboard website has information on how the test is taken and how to prepare, possibly some practice tests as well. For most courses there are also practice workbooks that specifically tell you the content of the test and how much time is spent on each section. Taking the class itself is helpful, but I suppose it's possible to pass with a decent score using just a workbook. For some courses (particularly AP European/US history) some of the information on the test may be something you've learned in previous previous regular/honors courses. Anyway, the test itself costs money, and since someone else has taken just the test I suppose it's possible for other subjects unless that was some sort of special case. If you decide to go for some AP credits, then I wish you luck.

Regards, Dr. Bean