I am trying to figure out how I can create a website that allows others to sign up for an account and have their own profile page like facebook, blogger, or this site lollol.
WordPress and many other social media software packages have this feature, though the theme you choose may or may not support it. Buddy Press is built on top of WordPress and is probably just what you want.
If you are asking how to do that yourself, you will need to use server side scripting and some sort of database program. I use PHP and MySQL. The database holds login information and other account details. Use the PHP to handle the logic and build the pages to be served.
The easiest way to make a page for each user is to store all content in the database. This includes posts, themes, or whatever the user can change. Then, create a page template with PHP that pulls the data from the database to fill the page when it is passed the username as input. You can use Apache mod_rewrite to make the URL pretty like www.yoursite.org/pages/JohnDoe instead of www.yoursite.org/pages/index.php?username=JohnDoe.
Check out using a content management system like Drupal or ExpressionEngine. These handle the PHP and MySQL parts for you.