You can check out MySQL doc here about installing on windows. From what I recall, it is essentially figuring out which distribution you need and running the installer. I think you want the "Install MySQL as a service" option, but I haven't done it in a while. Pretty self explanitory. I don't remember how hard ti was to get Apache, PHP and MySQL all to talk to each other.
If you want ease of use, ease of install, and better integration, I would suggest a package, like WAMP Server or XAMPP. I use WAMP and I think NogDog uses XAMPP.
WAMP has a system tray icon which gives you quick access to many useful features/tasks including: start/stop Apache or MySQL; edit all 3 config files; quick browse to your localhost root; and open your document root folder.
I definitely prefer it to the sort of ad hoc, throw all three together and hope they work.