If you have your own domain name, you will need a web host and a wordpress fresh instalation on.
Once this steps are accomplished, you will be able to write your own content as in a wordpress.com free account with more options to customize the appearance.

Check this link for more information about getting me to help you:

You Can, also, make a cheap website using  a free domain name provider and  blogger as  free hosting, like I did with the http://www.cheapsite.ga website!