There are multiple ways to solve this problem, but here's one that always suits my needs.
Guide all your URL requests through the index.php first and resolve the request in your PHP code second.
1) Use an .htaccess file to direct all URL's through index.php. You'll find one way here by the CodeIgniter framework and a more advanced explanation here. I recommend the CodeIgniter .htaccess guide first if you're inexperienced with .htaccess.
2) Second, use the $_SERVER variable in PHP to extract the URL. Probably with the help of the $_SERVER['REQUEST_URI'], you'll find '/username/' which you can then use to extract the user's data and serve it to them.
Good luck and beware of URL injections using this method.