AGK does not have any direct database functionality at all.
And, while it can open a
web page in a browser, it does not have a way to interact with the browser or 'know' anything that happens on it.
However, you can create forms in AppGameKit (using Text and Edit objects) and then interface with your domain server, usually using PHP pages, to store and/or retrieve things in a database.
My WIP has a simple register 'page' (it requests a user name for the database) and does a lot to send and retrieve game play information to my site (www.triassicgames.com).
It helps to know PHP, or at least a language that is supported on your web server that allows you to communicate with the database on your web server. I suppose, if it enabled on your server, you could use Perl or (shudders) ASP.
Cheers,
Ancient Lady
AGK Community Tester and AppGameKit Master