There are several APIs already out there which deal with High Scores, and most of them are free, and some even give you money if your game implements them and is famous enough.
But, if you plan on using a lot of Flash/PHP/MySQL in the future, the best book I have ever read on the topic is "The Flash and PHP Bible". It covers the basics of quite a lot, however, it doesn't get into deep detail in most topics, but at least you get a basic understanding of how things work.
You could ask your local Library to buy it, as after you have learned everything in it, it's not designed to really be a reference book. Once you know how the code works, all you need is a quick refresher or perhaps a few code snippets saved on your computer.
You might be able to find the source codes for the book online and learn from them. They should somewhere be on the "Wiley Publishing" website, I believe. EDIT:
http://eu.wiley.com/WileyCDA/WileyTi...470258241.html