Well, you can't.
Think about it! You can store usernames/passwords in your data objects and if they allow you to login and maintain a session for that user and use it to walk around apex pages and builtin forms why would you buy a salesforce license? You could operate a 1000 employees rig with just one administrative license and a site URL. For that reason salesforce does not allow you session control, it grants you one when you buy and expense a license.
For sites, you have to purchase either Customer Portal license or volume-based High Volume Customer Portal set and then use those to "promote" a contact into a login user with the above license. Then, when that user logs into site it has its own session.