You are already on the right track. MySQL is just the name of the database management system used here, so you would need to create a MySQL database in the Control Panel and then create a table to hold usernames and passwords. But that is the easy part.
You would need to build several PHP pages to handle the user registration process. A user could fill in a form (including specifying their own password), and then the data could be sent to the database. A user then "logs in" by entering the username and password they chose, and the two pieces of information are stored in either (a) session variables or (b) a cookie. Each page of your "members only" section must then check to see if the username and password match up to those in the database.
To let users edit their information, you could give them access to a page with a pre-populated form where they can change various values. The form could then be submitted and the data update.
Obviously, some form of error checking is needed during most steps of the process. Usernames don't really need to be unique, but the username/password combo must be. You will need to hold user information in a session when creating or editing records so that they don't have to type everything in again if they pick a username/password combination that is already in use.
If you are new to PHP and MySQL, this may all seem rather daunting; however, there really isn't much to it - especially if you treat the registration process as a separate project to the logging-in process. If it still seems like a big deal, some WYSIWYG software, such as Macromedia's Dreamweaver, have built-in scripts that can handle all this stuff for you.
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