Like a Facebook account URL address is
http://www.facebook.com/myname ???
Well in your case, you're probably not using a CMS, so the manual process root for this would be to create a new file directory attached to your root folder.
For example:
http://www.yourwebsite.com/index.html
Create a new folder with that person's name and you'll get:
http://www.yourwebsite.com/myname
Now to do what say Blogger does with their URLS:
http://myname.blogspot.com, that's basically the same process, only you're not creating a folder per say, you're creating a "sub domain."
I know it may seem simplistic, but here's an example again:
http://www.yourwebsite.com/index.html
Create a new sub domain with that person's name and you'll get:
http://myname.yourwebsite.com/index.html
Sub domains are great when you're wanting to create a sub website that is basically a sister website of the main website, or a subsidiary if you will. Sub websites do not necessarily have to resemble the main website in style or design, it can resemble a completely new idea in every respect.