I have a database set up using MySQL with a username and password, but once they enter their username and password and I verify it through the database, how are they still logged in going forward?
Assuming you are using PHP, this can be done with session data. A session lasts as long as the browser is open, unless you destroy the session sooner. You can store session variables, such as $_SESSION("userid"). Here's a pretty simple tutorial: http://php.about.com/od/advancedphp/ss/php_sessions.htm.
I think this is what you're looking for, if not please reply.