Flash doesn't connect to a database. Flash loads scripts that can access a database.

Basically instead of having (for example) an asp script that accesses a database and writes the content to html, you have the script write a set of variables so that it ends up looking like this:

&infoOne=Some info&infoTwo=Some more info&

Then flash loads the script and the variables are available to the flash player.

Flash 5 uses loadVariables() or loadVariablesNum(), if you've got Flash MX then you're better off with the custom LoadVars() object.

cheers.