You would use mod_rewrite which can allow you to "rewrite" the URL 😉
RewriteModule On
RewriteRule /(.*) /index.php
That would take all requests and move them to index.php. Sometimes this is referred to as a "bootstrapper" which routes all requests to whatever you want. Instead of just the username, I'd suggest using a URL like:
http://www.mysite.com/view_profile/CliftonH
Then you'd want to do a quick lookup for the userID based on the username passed.
RewriteModule On
RewriteRule /view_profile/(.*) view_profile.php?member_name=$1
mod_rewrite requires the Apache server. IIS and LightTPD do have similar modules (I think LightTPD actually calls it mod_rewrite) that do the same thing. You'll have to look into your server's documentation to see the proper implementation if you're not using Apache.