How server side page decide a request to a page is authorized?

It's normal case, user inputs a username with password, and after that the entire system can be accessed. Suppose I have a page a.php(or ASP), how can I restrict only the user that has been authorized can view a.php, for other user if they type (http://host/a.php) in browser, they will get an error?And furthermore, is it done thru cookie? If you can explain the details under the hood I would appreciate more :)
 
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